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If |z| = 6 and arg (z) = 3π/4, find z.

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If |z| = 6 and arg (z) = 3π/4, find z.

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We have, |z| = 6 and arg (z) = 3π/4

Let z = r(cosθ + i sinθ)

We know that, |z| = r = 6

And arg (z) = θ = 3π/4

Thus, z = r(cosθ + i sinθ) \(=6(cos\frac{3\pi}{4}+i\,sin\frac{3\pi}{4})\)

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