Write the argument of (1 + √3i) (cos θ+ isinθ)

Question

Write the argument of (1 + \(\sqrt{3i}\)) (cos θ+ isinθ)

Answer 1

Let z = (1 + √3i) (cosθ + isinθ) 

= cosθ + √3 sinθi² + isinθ + √3icos θ

= (cosθ - √3sin θ) + i(sinθ + √3cos θ) 

∴ Re(z) = cosθ - √3 sinθ 

And Im(z) = (sinθ+ √3cos θ) 

Now, argument of z is