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

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one month ago Anand Kumar Pandey
1583 Points
```							Dear StudentGiven,complex number is -3.Let r cos θ = -3 …(1)and r sin θ = 0 …(2)Squaring and adding (1) and (2), we getr^2cos^2θ + r^2sin^2θ = (-3)2Take r^2outside from L.H.S, we getr^2(cos^2θ + sin^2θ) = 9We know that, cos^2θ + sin^2θ = 1, r^2= 9r = 3 (Conventionally, r > 0)Now, subsbtitute the value of r in (1) and (2)3 cos θ = -3 and 3 sin θ = 0cos θ = -1 and sin θ = 0 θ = π the polar representation is,-3 = r cos θ + i r sin θ3 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
```
one month ago
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