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Express the given complex number (-3) in the polar form.

Express the given complex number (-3) in the polar form.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Given,
complex number is -3.

Let r cos θ = -3 …(1)

and r sin θ = 0 …(2)

Squaring and adding (1) and (2), we get

r^2cos^2θ + r^2sin^2θ = (-3)2

Take r^2outside from L.H.S, we get

r^2(cos^2θ + sin^2θ) = 9

We know that, cos^2θ + sin^2θ = 1,

r^2= 9

r = 3 (Conventionally, r > 0)

Now, subsbtitute the value of r in (1) and (2)

3 cos θ = -3 and 3 sin θ = 0

cos θ = -1 and sin θ = 0

θ = π

the polar representation is,

-3 = r cos θ + i r sin θ

3 cos π + 3 sin π = 3(cos π + i sin π)

Thus, the required polar form is 3 cos π+ 3i sin π = 3(cos π+i sin π)

Thanks

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