Question

How do you add `(5+5i)+(-3+i)` in trigonometric form?

Answer 1

`(5+5i)+(-3+i)=2sqrt10(cos(5/4)+isin(5/4))`

Explanation:

`(5+5i)+(-3+i)=(5-3)+(5i+i)=2+6i`

Any complex number of the form `a+bi, a,b in RR` may be written in its mod-arg form `r(cosvartheta+isinvartheta)` where `r=sqrt(a^2+b^2)` and `vartheta =arctan (b"/"a)`

`r=sqrt(2^2+6^2)=sqrt(40)=2sqrt10`

`vartheta=arctan (6/2)=arctan3approx5/4`

`therefore 2+6i = 2sqrt10(cos(5/4)+isin(5/4))`