How do you write the complex number in trigonometric form 5+2i?

1 Answer
Nov 19, 2016

5+2i=sqrt29costheta+isqrt29sintheta, where theta=tan^(-1)(2/5)

Explanation:

A number a+ib can be written in trigonometric form as

rcostheta+irsintheta.

As rcostheta=a and rsintheta=b, squaring and adding them we get r^2=a^2+b^2.

As such for 5+2i, r=sqrt(5^2+2^2)=sqrt(25+4)=sqrt29

and costheta=5/sqrt29 and sintheta=2/sqrt29

i.e. tantheta=2/5 and theta=tan^(-1)(2/5)

Hence in trigonometric form

5+2i=sqrt29costheta+isqrt29sintheta, where theta=tan^(-1)(2/5)