Question

Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

2i

Answer 1

Let z = 2i = 0 + 2i

∴ a = 0, b = 2

∴ z lies on positive imaginary Y-axis

∴ |z| = r

= ${\displaystyle \sqrt{{\text{a}}^2+{\text{b}}^2}}$

= ${\displaystyle \sqrt{0^2+2^2}}$

= ${\displaystyle \sqrt{0+4}}$

= 2

∴ amp (z) = θ = ${\displaystyle \frac{\pi }{2}}$

∴ θ = 90° = ${\displaystyle \frac{\pi }{2}}$

∴ the polar form of z = r(cos θ + i sin θ)

= 2(cos 90° + i sin 90°)

= ${\displaystyle 2(\cos \frac{\pi }{2}+\text{i}\sin \frac{\pi }{2})}$