Question

How do you add `(-7-5i)` and `(-2+2i)` in trigonometric form?

Answer 1

`z=9.49(cos(18.43^@)+isin(18.43))` or simply `(9.49,18.43^@)`

Explanation:

Strategy. First add them up, while they are still in rectangular form. Then convert the single term rectangular number into trigonometric form. Choose degrees or radians for the angle. I choose degrees.

Step 1. Add the two rectangular complex numbers. The result will be in standard rectangular form `a+bi` or `(a,b)`

`(-7-5i)+(-2+2i)=(-7-2-5i+2i)=-9-3i`

Here, `a=-9` and `b=-3`

Step 2. Given the conversion formulas, translate to trig form, which is of the form `z=r(cos(theta)+isin(theta))` or in polar form `(r,theta)`

`theta=tan^-1(b/a)=tan^-1((-3)/-9)=tan^-1(1/3)~~18.43^@`

`r=sqrt(a^2+b^2)=sqrt((-9)^2+(-3)^2)=sqrt(90)~~9.49`

`z=9.49(cos(18.43^@)+isin(18.43))` or simply `(9.49,18.43^@)`