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

= `sqrt("a"^2 + "b"^2)`

= `sqrt(0^2 + 2^2)`

= `sqrt(0 + 4)`

= 2

∴ amp (z) = θ = `pi/2`

∴ θ = 90° = `pi/2`

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

= 2(cos 90° + i sin 90°)

= `2(cos  pi/2 + "i" sin  pi/2)`