Question

How do you add `(2-3i)` and `(12-2i)` in trigonometric form?

Answer 1

`sqrt221(cos(0.343)-isin(0.343))`

Explanation:

A complex number z = x +iy can be expressed in trig. form as shown.

`z=x+iy=r(costheta+isintheta)" where"`

`•r=sqrt(x^2+y^2)" and " theta=tan^-1(y/x)`

Now to get this sum in trig form we have to add the numbers together and then convert to trig.

`rArr(2-3i)+(12-2i)=14-5i`

Using x = 14 and y = -5 , convert to trig form.

`rArrr=sqrt(14^2+(-5)^2)=sqrt221" does not simplify further"`

and `theta=tan^-1(-5/14)≈-0.343" radians"`

`rArr14-5i=sqrt221(cos(-0.343)+isin(-0.343))`

using `cos(-theta)=costheta" and "sin(-theta)=-sintheta`

we can also express in trig form as

`14-5i=sqrt221(cos(0.343)-isin(0.343))`