Question

What is the trigonometric form of `(-2+10i)(3+3i)`?

Answer 1

`12sqrt(13)(cos(tan^-1(-2/3))+isin(tan^-1(-2/3)))~~43.267(cos(-0.588)+isin(-0.588))`

Explanation:

`(-2+10i)(3+3i)=-6+30i-6i+30i^2=-36+24i`

Trigonometric form: `r(isin(theta)+cos(theta))`
Rectangular form: `a+bi`
`r=sqrt(a^2+b^2)=sqrt(36^2+24^2)~~43.267`
`theta=tan^-1(b/a)=tan^-1(24/-36)`
`=tan^-1(-2/3)~~-0.588 (radians)`

`12sqrt(13)(cos(tan^-1(-2/3))+isin(tan^-1(-2/3)))`