Question

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

Answer 1

`sqrt10(cos(-1.25)+isin(-1.25) )`

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))`