What is the trigonometric form of (−2+10i)(3+3i)?

1 Answer
Martin C.
Mar 28, 2018

12√13(cos(tan−1(−23))+isin(tan−1(−23)))≈43.267(cos(−0.588)+isin(−0.588))

Explanation:

(−2+10i)(3+3i)=−6+30i−6i+30i2=−36+24i

Trigonometric form: r(isin(θ)+cos(θ))
Rectangular form: a+bi
r=√a2+b2=√362+242≈43.267
θ=tan−1(ba)=tan−1(24−36)
=tan−1(−23)≈−0.588(radians)

12√13(cos(tan−1(−23))+isin(tan−1(−23)))

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