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

1 Answer
Jim G.
May 17, 2016

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))

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