Question

Find the modulus and amplitude for following complex number: 1 + i√3

Answer 1

Let z = 1 + i√3

a = 1, b = √3, i.e. a > 0, b > 0

|z| = \(\sqrt{a^2+b^2}=\sqrt{162+(\sqrt3)^2}=\sqrt{1+3}=2\)

Here, (1, √3) lies in 1st quadrant.

amp(z) = tan^-1\((\frac{b}a)\) = tan^-1√3 = \(\frac{\pi}3\)