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

1 Answer
Feb 28, 2017

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.