# What is the trigonometric form of # (1-3i) #?

##### 1 Answer

May 2, 2016

#### Explanation:

Given a complex number z = x + iy , then in trig.form it is written

z =

#r(costheta + isintheta)# where

#|z|=|x+iy|=r=sqrt(x^2+y^2)# and

#theta=tan^-1(y/x)# here x = 1 and y = - 3

#rArr r=sqrt(1^2+(-3)^2)=sqrt10# and

#theta=tan^-1(-3)=-1.25" radians "#

#rArr(1-3i)=sqrt10(cos(-1.25)+isin(-1.25))#