Question

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

Answer 1

As explained below

Explanation:

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.