Algebra Examples

${(2 (\cos (\frac{π}{4}) + i \sin (\frac{π}{4})))}^{4}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

${(2 (\frac{\sqrt{2}}{2} + i \sin (\frac{π}{4})))}^{4}$

Step 1.1.2

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

${(2 (\frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}))}^{4}$

Step 1.1.3

Combine $i$ and $\frac{\sqrt{2}}{2}$ .

${(2 (\frac{\sqrt{2}}{2} + \frac{i \sqrt{2}}{2}))}^{4}$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

${(2 \frac{\sqrt{2}}{2} + 2 \frac{i \sqrt{2}}{2})}^{4}$

Step 1.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1

Cancel the common factor.

${(2 \frac{\sqrt{2}}{2} + 2 \frac{i \sqrt{2}}{2})}^{4}$

Step 1.2.2.2

Rewrite the expression.

${(\sqrt{2} + 2 \frac{i \sqrt{2}}{2})}^{4}$

Step 1.2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1

Cancel the common factor.

${(\sqrt{2} + 2 \frac{i \sqrt{2}}{2})}^{4}$

Step 1.2.3.2

Rewrite the expression.

${(\sqrt{2} + i \sqrt{2})}^{4}$

Step 2

Use the Binomial Theorem.

${\sqrt{2}}^{4} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Rewrite ${\sqrt{2}}^{4}$ as $2^{2}$ .

Tap for more steps...

Step 3.1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

${(2^{\frac{1}{2}})}^{4} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{\frac{1}{2} \cdot 4} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.3

Combine $\frac{1}{2}$ and $4$ .

$2^{\frac{4}{2}} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.4

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 3.1.1.4.1

Factor $2$ out of $4$ .

$2^{\frac{2 \cdot 2}{2}} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.4.2

Cancel the common factors.

Tap for more steps...

Step 3.1.1.4.2.1

Factor $2$ out of $2$ .

$2^{\frac{2 \cdot 2}{2 (1)}} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.4.2.2

Cancel the common factor.

$2^{\frac{2 \cdot 2}{2 \cdot 1}} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.4.2.3

Rewrite the expression.

$2^{\frac{2}{1}} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.1.4.2.4

Divide $2$ by $1$ .

$2^{2} + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.2

Raise $2$ to the power of $2$ .

$4 + 4 {\sqrt{2}}^{3} (i \sqrt{2}) + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.3

Multiply ${\sqrt{2}}^{3}$ by $\sqrt{2}$ by adding the exponents.

Tap for more steps...

Step 3.1.3.1

Move $\sqrt{2}$ .

$4 + 4 (\sqrt{2} {\sqrt{2}}^{3}) i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.3.2

Multiply $\sqrt{2}$ by ${\sqrt{2}}^{3}$ .

Tap for more steps...

Step 3.1.3.2.1

Raise $\sqrt{2}$ to the power of $1$ .

$4 + 4 ({\sqrt{2}}^{1} {\sqrt{2}}^{3}) i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 + 4 {\sqrt{2}}^{1 + 3} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.3.3

Add $1$ and $3$ .

$4 + 4 {\sqrt{2}}^{4} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4

Rewrite ${\sqrt{2}}^{4}$ as $2^{2}$ .

Tap for more steps...

Step 3.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 + 4 {(2^{\frac{1}{2}})}^{4} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 + 4 \cdot 2^{\frac{1}{2} \cdot 4} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.3

Combine $\frac{1}{2}$ and $4$ .

$4 + 4 \cdot 2^{\frac{4}{2}} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.4

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 3.1.4.4.1

Factor $2$ out of $4$ .

$4 + 4 \cdot 2^{\frac{2 \cdot 2}{2}} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.4.2

Cancel the common factors.

Tap for more steps...

Step 3.1.4.4.2.1

Factor $2$ out of $2$ .

$4 + 4 \cdot 2^{\frac{2 \cdot 2}{2 (1)}} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.4.2.2

Cancel the common factor.

$4 + 4 \cdot 2^{\frac{2 \cdot 2}{2 \cdot 1}} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.4.2.3

Rewrite the expression.

$4 + 4 \cdot 2^{\frac{2}{1}} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.4.4.2.4

Divide $2$ by $1$ .

$4 + 4 \cdot 2^{2} i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.5

Raise $2$ to the power of $2$ .

$4 + 4 \cdot 4 i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.6

Multiply $4$ by $4$ .

$4 + 16 i + 6 {\sqrt{2}}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.7

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Tap for more steps...

Step 3.1.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 + 16 i + 6 {(2^{\frac{1}{2}})}^{2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 + 16 i + 6 \cdot 2^{\frac{1}{2} \cdot 2} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.7.3

Combine $\frac{1}{2}$ and $2$ .

$4 + 16 i + 6 \cdot 2^{\frac{2}{2}} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.7.4.1

Cancel the common factor.

$4 + 16 i + 6 \cdot 2^{\frac{2}{2}} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.7.4.2

Rewrite the expression.

$4 + 16 i + 6 \cdot 2^{1} {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.7.5

Evaluate the exponent.

$4 + 16 i + 6 \cdot 2 {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.8

Multiply $6$ by $2$ .

$4 + 16 i + 12 {(i \sqrt{2})}^{2} + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.9

Apply the product rule to $i \sqrt{2}$ .

$4 + 16 i + 12 (i^{2} {\sqrt{2}}^{2}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.10

Rewrite $i^{2}$ as $- 1$ .

$4 + 16 i + 12 (- {\sqrt{2}}^{2}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.11

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Tap for more steps...

Step 3.1.11.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 + 16 i + 12 (- {(2^{\frac{1}{2}})}^{2}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.11.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 + 16 i + 12 (- 2^{\frac{1}{2} \cdot 2}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.11.3

Combine $\frac{1}{2}$ and $2$ .

$4 + 16 i + 12 (- 2^{\frac{2}{2}}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.11.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.11.4.1

Cancel the common factor.

$4 + 16 i + 12 (- 2^{\frac{2}{2}}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.11.4.2

Rewrite the expression.

$4 + 16 i + 12 (- 2^{1}) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.11.5

Evaluate the exponent.

$4 + 16 i + 12 (- 1 \cdot 2) + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.12

Multiply $12 (- 1 \cdot 2)$ .

Tap for more steps...

Step 3.1.12.1

Multiply $- 1$ by $2$ .

$4 + 16 i + 12 \cdot - 2 + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.12.2

Multiply $12$ by $- 2$ .

$4 + 16 i - 24 + 4 \sqrt{2} {(i \sqrt{2})}^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.13

Apply the product rule to $i \sqrt{2}$ .

$4 + 16 i - 24 + 4 \sqrt{2} (i^{3} {\sqrt{2}}^{3}) + {(i \sqrt{2})}^{4}$

Step 3.1.14

Multiply $\sqrt{2}$ by ${\sqrt{2}}^{3}$ by adding the exponents.

Tap for more steps...

Step 3.1.14.1

Move ${\sqrt{2}}^{3}$ .

$4 + 16 i - 24 + 4 ({\sqrt{2}}^{3} \sqrt{2}) i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.14.2

Multiply ${\sqrt{2}}^{3}$ by $\sqrt{2}$ .

Tap for more steps...

Step 3.1.14.2.1

Raise $\sqrt{2}$ to the power of $1$ .

$4 + 16 i - 24 + 4 ({\sqrt{2}}^{3} {\sqrt{2}}^{1}) i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.14.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 + 16 i - 24 + 4 {\sqrt{2}}^{3 + 1} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.14.3

Add $3$ and $1$ .

$4 + 16 i - 24 + 4 {\sqrt{2}}^{4} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15

Rewrite ${\sqrt{2}}^{4}$ as $2^{2}$ .

Tap for more steps...

Step 3.1.15.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 + 16 i - 24 + 4 {(2^{\frac{1}{2}})}^{4} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 + 16 i - 24 + 4 \cdot 2^{\frac{1}{2} \cdot 4} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.3

Combine $\frac{1}{2}$ and $4$ .

$4 + 16 i - 24 + 4 \cdot 2^{\frac{4}{2}} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.4

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 3.1.15.4.1

Factor $2$ out of $4$ .

$4 + 16 i - 24 + 4 \cdot 2^{\frac{2 \cdot 2}{2}} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.4.2

Cancel the common factors.

Tap for more steps...

Step 3.1.15.4.2.1

Factor $2$ out of $2$ .

$4 + 16 i - 24 + 4 \cdot 2^{\frac{2 \cdot 2}{2 (1)}} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.4.2.2

Cancel the common factor.

$4 + 16 i - 24 + 4 \cdot 2^{\frac{2 \cdot 2}{2 \cdot 1}} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.4.2.3

Rewrite the expression.

$4 + 16 i - 24 + 4 \cdot 2^{\frac{2}{1}} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.15.4.2.4

Divide $2$ by $1$ .

$4 + 16 i - 24 + 4 \cdot 2^{2} i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.16

Raise $2$ to the power of $2$ .

$4 + 16 i - 24 + 4 \cdot 4 i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.17

Multiply $4$ by $4$ .

$4 + 16 i - 24 + 16 i^{3} + {(i \sqrt{2})}^{4}$

Step 3.1.18

Factor out $i^{2}$ .

$4 + 16 i - 24 + 16 (i^{2} \cdot i) + {(i \sqrt{2})}^{4}$

Step 3.1.19

Rewrite $i^{2}$ as $- 1$ .

$4 + 16 i - 24 + 16 (- 1 \cdot i) + {(i \sqrt{2})}^{4}$

Step 3.1.20

Rewrite $- 1 i$ as $- i$ .

$4 + 16 i - 24 + 16 (- i) + {(i \sqrt{2})}^{4}$

Step 3.1.21

Multiply $- 1$ by $16$ .

$4 + 16 i - 24 - 16 i + {(i \sqrt{2})}^{4}$

Step 3.1.22

Apply the product rule to $i \sqrt{2}$ .

$4 + 16 i - 24 - 16 i + i^{4} {\sqrt{2}}^{4}$

Step 3.1.23

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 3.1.23.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$4 + 16 i - 24 - 16 i + {(i^{2})}^{2} {\sqrt{2}}^{4}$

Step 3.1.23.2

Rewrite $i^{2}$ as $- 1$ .

$4 + 16 i - 24 - 16 i + {(- 1)}^{2} {\sqrt{2}}^{4}$

Step 3.1.23.3

Raise $- 1$ to the power of $2$ .

$4 + 16 i - 24 - 16 i + 1 {\sqrt{2}}^{4}$

Step 3.1.24

Multiply ${\sqrt{2}}^{4}$ by $1$ .

$4 + 16 i - 24 - 16 i + {\sqrt{2}}^{4}$

Step 3.1.25

Rewrite ${\sqrt{2}}^{4}$ as $2^{2}$ .

Tap for more steps...

Step 3.1.25.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 + 16 i - 24 - 16 i + {(2^{\frac{1}{2}})}^{4}$

Step 3.1.25.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 + 16 i - 24 - 16 i + 2^{\frac{1}{2} \cdot 4}$

Step 3.1.25.3

Combine $\frac{1}{2}$ and $4$ .

$4 + 16 i - 24 - 16 i + 2^{\frac{4}{2}}$

Step 3.1.25.4

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 3.1.25.4.1

Factor $2$ out of $4$ .

$4 + 16 i - 24 - 16 i + 2^{\frac{2 \cdot 2}{2}}$

Step 3.1.25.4.2

Cancel the common factors.

Tap for more steps...

Step 3.1.25.4.2.1

Factor $2$ out of $2$ .

$4 + 16 i - 24 - 16 i + 2^{\frac{2 \cdot 2}{2 (1)}}$

Step 3.1.25.4.2.2

Cancel the common factor.

$4 + 16 i - 24 - 16 i + 2^{\frac{2 \cdot 2}{2 \cdot 1}}$

Step 3.1.25.4.2.3

Rewrite the expression.

$4 + 16 i - 24 - 16 i + 2^{\frac{2}{1}}$

Step 3.1.25.4.2.4

Divide $2$ by $1$ .

$4 + 16 i - 24 - 16 i + 2^{2}$

Step 3.1.26

Raise $2$ to the power of $2$ .

$4 + 16 i - 24 - 16 i + 4$

Step 3.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.1

Subtract $24$ from $4$ .

$- 20 + 16 i - 16 i + 4$

Step 3.2.2

Add $- 20$ and $4$ .

$- 16 + 16 i - 16 i$

Step 3.2.3

Subtract $16 i$ from $16 i$ .

$- 16 + 0$

Step 3.2.4

Add $- 16$ and $0$ .

$- 16$