How do you divide 4−8i9+i in trigonometric form?

1 Answer
Yonas Yohannes
Feb 13, 2016

R=.337+−915i

Explanation:

R=C1C2, where C1=4−8i and C2=9+i
Convert each complex number to its polar form:
C1=|C1|∠θ1andC2=|C2|∣∠θ2
Then, R=|C1||C2|∠θ1−θ2
C1=√42+(−8)2=√80;C2=√92+(1)2=√82
θ1=tan−1(−2);θ2=tan−1(19);
θR=θ1−θ2=tan−1(−2)−tan−1(19)=−1.218 rads
Thus R=.975∠(θR=−1.218) this is now in the polar form
R=r∠θR;r=.975 the magnitude of R,θR=−69.775o
Now you can convert back to the rectangular coordinate
R=rx+ry;Rx=|r|cosθR+|r|sinθR
rx=.975cos69.8≈.337;ry=.975sin(−69.8)≈−.915
R≈.337+−915i

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