Precalculus Examples

32 (cos (280 °) + i sin (280 °))

$32 (\cos (280 °) + i \sin (280 °))$

Step 1

Set

32 (cos (280 °) + i sin (280 °))

$32 (\cos (280 °) + i \sin (280 °))$ equal to

0

$0$ .

32 (cos (280 °) + i sin (280 °)) = 0

$32 (\cos (280 °) + i \sin (280 °)) = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Simplify

32 (cos (280 °) + i sin (280 °))

$32 (\cos (280 °) + i \sin (280 °))$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Evaluate

cos (280 °)

$\cos (280 °)$ .

32 (0.17364817 + i sin (280 °)) = 0

$32 (0.17364817 + i \sin (280 °)) = 0$

Step 2.1.1.2

Evaluate

sin (280 °)

$\sin (280 °)$ .

32 (0.17364817 + i \cdot - 0.98480775) = 0

$32 (0.17364817 + i \cdot - 0.98480775) = 0$

Step 2.1.1.3

Move

- 0.98480775

$- 0.98480775$ to the left of

i

$i$ .

32 (0.17364817 - 0.98480775 i) = 0

$32 (0.17364817 - 0.98480775 i) = 0$

32 (0.17364817 - 0.98480775 i) = 0

$32 (0.17364817 - 0.98480775 i) = 0$

Step 2.1.2

Simplify by multiplying through.

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Step 2.1.2.1

Apply the distributive property.

32 \cdot 0.17364817 + 32 (- 0.98480775 i) = 0

$32 \cdot 0.17364817 + 32 (- 0.98480775 i) = 0$

Step 2.1.2.2

Multiply.

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Step 2.1.2.2.1

Multiply

32

$32$ by

0.17364817

$0.17364817$ .

5.55674168 + 32 (- 0.98480775 i) = 0

$5.55674168 + 32 (- 0.98480775 i) = 0$

Step 2.1.2.2.2

Multiply

- 0.98480775

$- 0.98480775$ by

32

$32$ .

5.55674168 - 31.51384809 i = 0

$5.55674168 - 31.51384809 i = 0$

5.55674168 - 31.51384809 i = 0

$5.55674168 - 31.51384809 i = 0$

5.55674168 - 31.51384809 i = 0

$5.55674168 - 31.51384809 i = 0$

5.55674168 - 31.51384809 i = 0

$5.55674168 - 31.51384809 i = 0$

Step 2.2

Since

5.55674168 - 31.51384809 i \neq 0

$5.55674168 - 31.51384809 i \neq 0$ , there are no solutions.

No solution

No solution

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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