Question

Addition operations in polar form? `sqrt(18)(cos175°+isin175°)+(cos40°+isin40°)`

What would be the best way to perform addition operations in the polar form? Convert to cartesian form then add Re/Im components or is there another way? I only know how to multiply/divide in polar form.

Answer 1

`color(brown)(=> -3.4605 + 1.0126 i`

Explanation:

`z= a+bi= r (costheta+isintheta)`

`r=sqrt(a^2+b^2), " " theta=tan^-1(b/a)`

`r_1(cos(theta_1)+isin(theta_2))+r_2(cos(theta_2)+isin(theta_2))=r_1cos(theta_1)+r_2cos(theta_2)+i(r_1sin(theta_1)+r_2sin(theta_2))`
`sqrt18(cos 175 + i sin 175) + 9cos 40 + i sin 40)`

`=> (sqrt18 cos 175 + cos 40) + i (sqrt18 sin 175 + sin 40)`

`=>( -4.2265 + 0.7660) + i (0.3698 + 0.6428)`

`color(brown)(=> -3.4605 + 1.0126 i`