How do you write # -3+4i# in trigonometric form?

1 Answer
Topscooter
Jan 9, 2016

You need the module and the argument of the complex number.

Explanation:

In order to have the trigonometric form of this complex number, we first need its module. Let's say #z = -3 +4i#.

#absz = sqrt((-3)^2 + 4^2) = sqrt(25) = 5#

In #RR^2#, this complex number is represented by #(-3,4)#. So the argument of this complex number seen as a vector in #RR^2# is #arctan(4/-3) + pi = -arctan(4/3) + pi#. We add #pi# because #-3 < 0#.

So the trigonometric form of this complex number is #5e^(i(pi - arctan(4/3))#

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