Answer:
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^2sin2θ = (-3)^2
Take r2 outside from L.H.S, we get
r^2(cos^2θ + sin^2θ) = 9
We know that, cos^2θ + sin^2θ = 1, then the above equation becomes,
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
Therefore, θ = π
Hence, 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)
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