Precalculus Examples

$z = 4 (\cos (50) + i \sin (50))$ , $w = \cos (340) + i \sin (340)$

Step 1

Reduce the system.

$z = 4 (\cos (50) + i \sin (50)), w = \cos (340) + i \sin (340)$

Step 2

Simplify the right side.

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Step 2.1

Simplify $4 (\cos (50) + i \sin (50))$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Evaluate $\cos (50)$ .

$z = 4 (0.6427876 + i \sin (50))$

$w = \cos (340) + i \sin (340)$

Step 2.1.1.2

Evaluate $\sin (50)$ .

$z = 4 (0.6427876 + i \cdot 0.76604444)$

$w = \cos (340) + i \sin (340)$

Step 2.1.1.3

Move $0.76604444$ to the left of $i$ .

$z = 4 (0.6427876 + 0.76604444 i)$

$w = \cos (340) + i \sin (340)$

$z = 4 (0.6427876 + 0.76604444 i)$

$w = \cos (340) + i \sin (340)$

Step 2.1.2

Simplify by multiplying through.

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Step 2.1.2.1

Apply the distributive property.

$z = 4 \cdot 0.6427876 + 4 (0.76604444 i)$

$w = \cos (340) + i \sin (340)$

Step 2.1.2.2

Multiply.

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Step 2.1.2.2.1

Multiply $4$ by $0.6427876$ .

$z = 2.57115043 + 4 (0.76604444 i)$

$w = \cos (340) + i \sin (340)$

Step 2.1.2.2.2

Multiply $0.76604444$ by $4$ .

$z = 2.57115043 + 3.06417777 i$

$w = \cos (340) + i \sin (340)$

$z = 2.57115043 + 3.06417777 i$

$w = \cos (340) + i \sin (340)$

$z = 2.57115043 + 3.06417777 i$

$w = \cos (340) + i \sin (340)$

$z = 2.57115043 + 3.06417777 i$

$w = \cos (340) + i \sin (340)$

$z = 2.57115043 + 3.06417777 i$

$w = \cos (340) + i \sin (340)$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Evaluate $\cos (340)$ .

$w = 0.93969262 + i \sin (340)$

$z = 2.57115043 + 3.06417777 i$

Step 3.1.2

Evaluate $\sin (340)$ .

$w = 0.93969262 + i \cdot - 0.34202014$

$z = 2.57115043 + 3.06417777 i$

Step 3.1.3

Move $- 0.34202014$ to the left of $i$ .

$w = 0.93969262 - 0.34202014 i$

$z = 2.57115043 + 3.06417777 i$

$w = 0.93969262 - 0.34202014 i$

$z = 2.57115043 + 3.06417777 i$

$w = 0.93969262 - 0.34202014 i$

$z = 2.57115043 + 3.06417777 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$