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

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Answer 1 · 2017-02-28T19:57:53

As explained below

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

|z|= $sqrt (1^2 +8^2)= sqrt65$

Now write z= $sqrt65 (-1/sqrt65 +i8/sqrt65 )$

Now consider an angle $theta$ , such that $cos theta= -1/sqrt65$ and $sin theta = 8/sqrt65$ . This implies $tan theta =8/-1 = -8$

Now z can be expressed as $sqrt65 (cos theta +i sin theta)$ , where $theta= tan^-1 -8 or arc tan -8$

This is the required trignometric form.

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