Question

How do you add `(-1+3i)+(7-3i)` in trigonometric form?

Answer 1

Adding in rectangular form then converting to trigonometric form gives
`color(white)("XXX")6(cos(0)+isin(0))`

Explanation:

Confession: I don't know any easy way to do the addition in trigonometric form (multiplication and division is relatively easy).

However we can add:
`color(white)("XXX")(-1+3i)+(7-3i)`
`color(white)("XXXXXX")=(-1+7)+(3i-3i)`
`color(white)("XXXXXX")=6+0i`

which translates easily into trigonometric form `r(cos(theta)+isin(theta))`
with `r=sqrt(6^2+0^2) = 6`
and `theta = arctan(0/6)= arctan(0) = 0`