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

1 Answer
Andy Y.
May 31, 2017

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(θ)+isin(θ)) or in polar form (r,θ)

θ=tan−1(ba)=tan−1(−3−9)=tan−1(13)≈18.43∘

r=√a2+b2=√(−9)2+(−3)2=√90≈9.49

z=9.49(cos(18.43∘)+isin(18.43)) or simply (9.49,18.43∘)

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