Calculus Examples

$z = i + \sqrt{- 3 x - (- 3)} + \sqrt{- 9} + 11$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 1$ by $- 3$ .

$z = i + \sqrt{- 3 x + 3} + \sqrt{- 9} + 11$

Step 1.2

Factor $3$ out of $- 3 x + 3$ .

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Step 1.2.1

Factor $3$ out of $- 3 x$ .

$z = i + \sqrt{3 (- x) + 3} + \sqrt{- 9} + 11$

Step 1.2.2

Factor $3$ out of $3$ .

$z = i + \sqrt{3 (- x) + 3 (1)} + \sqrt{- 9} + 11$

Step 1.2.3

Factor $3$ out of $3 (- x) + 3 (1)$ .

$z = i + \sqrt{3 (- x + 1)} + \sqrt{- 9} + 11$

Step 1.3

Rewrite $- 9$ as $- 1 (9)$ .

$z = i + \sqrt{3 (- x + 1)} + \sqrt{- 1 (9)} + 11$

Step 1.4

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$z = i + \sqrt{3 (- x + 1)} + \sqrt{- 1} \cdot \sqrt{9} + 11$

Step 1.5

Rewrite $\sqrt{- 1}$ as $i$ .

$z = i + \sqrt{3 (- x + 1)} + i \cdot \sqrt{9} + 11$

Step 1.6

Rewrite $9$ as $3^{2}$ .

$z = i + \sqrt{3 (- x + 1)} + i \cdot \sqrt{3^{2}} + 11$

Step 1.7

Pull terms out from under the radical, assuming positive real numbers.

$z = i + \sqrt{3 (- x + 1)} + i \cdot 3 + 11$

Step 1.8

Move $3$ to the left of $i$ .

$z = i + \sqrt{3 (- x + 1)} + 3 i + 11$

Step 2

Add $i$ and $3 i$ .

$z = 4 i + \sqrt{3 (- x + 1)} + 11$