How do you divide 2i−7−2i−8 in trigonometric form?

1 Answer
Douglas K.
Jun 16, 2017

Division in trigonometric form is:
r1(cos(θ1)+isin(θ1))r2(cos(θ2)+isin(θ2))=r1r2(cos(θ1−θ2)+isin(θ1−θ2))

Explanation:

Given: 2i−7−2i−8

r1=√(−7)2+22

r1=√53

To find the value of θ1, we must observe that the real part is negative and the imaginary part is positive; this places the angle in the 2nd quadrant:

θ1=π+tan−1(2−7)

θ1=π−tan−1(27)

Moving on to r2:

r2=√(−8)2+(−2)2

r2=√68

To find the value of θ2, we must observe that the real part is negative and the imaginary part is negative; this places the angle in the 3nd quadrant:

θ2=π+tan−1(−2−8)

θ2=π+tan−1(14)

2i−7−2i−8=√5368(cos(−tan−1(27)−tan−1(14))+isin(−tan−1(27)−tan−1(14)))

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