How do you write the complex number in trigonometric form #3-3i#?

1 Answer
Dreamer.N
May 5, 2018

In the trigonometric form we will have: #3sqrt(2)(cos(-pi/4)+isin(-pi/4))#

Explanation:

We have
3-3i
Taking out 3 as common we have 3(1-i)
Now multiplying and diving by #sqrt2# we get, 3 #sqrt2#(1/ #sqrt2#- i/ #sqrt2#)

Now we have to find the argument of the given complex number which is tan(1/#sqrt2#/(-1/#sqrt2#)) whixh comes out to be -#pi#/4 .Since the sin part is negative but cos part is positive so it lies in quadrant 4, implying that argument is #-pi/4#.
Hence
#3sqrt(2)(cos(-pi/4)+isin(-pi/4))# is the answer.

Hope it helps!!

Related questions
See all questions in The Trigonometric Form of Complex Numbers
Impact of this question
3156 views around the world
You can reuse this answer
Creative Commons License