What is the trigonometric form of $(- 1 + 8 i)$ $(-1+8i)$ ?

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What is the trigonometric form of $(- 1 + 8 i)$ $(-1+8i)$ ?

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Answer 1 · 2017-02-28T19:57:53

As explained below

Explanation:

If denoted by z = -1+8i, then

|z|= $\sqrt{1^{2} + 8^{2}} = \sqrt{65}$ $sqrt (1^2 +8^2)= sqrt65$

Now write z= $\sqrt{65} (- \frac{1}{\sqrt{65}} + i \frac{8}{\sqrt{65}})$ $sqrt65 (-1/sqrt65 +i8/sqrt65 )$

Now consider an angle $θ$ $theta$ , such that $cos θ = - \frac{1}{\sqrt{65}}$ $cos theta= -1/sqrt65$ and $sin θ = \frac{8}{\sqrt{65}}$ $sin theta = 8/sqrt65$ . This implies $tan θ = \frac{8}{- 1} = - 8$ $tan theta =8/-1 = -8$

Now z can be expressed as $\sqrt{65} (cos θ + i sin θ)$ $sqrt65 (cos theta +i sin theta)$ , where $θ = {tan}^{- 1} - 8 or a r c tan - 8$ $theta= tan^-1 -8 or arc tan -8$

This is the required trignometric form.

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What is the trigonometric form of $(- 1 + 8 i)$ $(-1+8i)$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

What is the trigonometric form of (−1+8i) (-1+8i) ?

1 Answer

Explanation:

Related questions

Impact of this question

What is the trigonometric form of $(- 1 + 8 i)$ $(-1+8i)$ ?