How do you add (1−5i)+(−2+i) in trigonometric form?

1 Answer
Leland Adriano Alejandro
Feb 21, 2016

√17[cos(tan−1(−4−1))+isin(tan−1(−4−1))]
√17[cos(4.4674103172578)+isin(4.4674103172578)] Radian

√17[cos(255.96375653207∘)+isin(255.96375653207∘)]

Explanation:

First we add the complex numbers
(1−5i)+(−2+i)=

=(1−2)+(−5i+i)

=−1−4i

Convert to trigonometric form

for complex number a+ib

a+ib=√a2+b2⋅[cos(tan−1(ba))+isin(tan−1(ba))]

so we let a=−1 and b=−4

−1−4i=
√(−1)2+(−4)2⋅[cos(tan−1(−4−1))+isin(tan−1(−4−1))]

In the complex rectangular coordinate system, this is located at the 3rd quadrant

√17[cos(tan−1(−4−1))+isin(tan−1(−4−1))]
√17[cos(4.4674103172578)+isin(4.4674103172578)] Radian

√17[cos(255.96375653207∘)+isin(255.96375653207∘)]

have a nice day !

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