Question

Represent the complex number z= -2-2i in the polar form.

Answer 1

Complex numbers polar form is z = rcosΘ + i rsin Θ

The complex number z = x + iy so

x = rcosΘ ; y = rsin Θ and tanΘ = (yx)

∴ z = r(rcosΘ + i sin Θ) is the polar form (or the trigonometric form) of a complex number.

The polar form of the complex number |z|= x2+y2−−−−−−√

|z| is the modulus of z and Θ is called the argument (or amplitude) of z which is denoted by arg z.

For any complex number z ≠ 0, there corresponds only one value of Θ in 0 ≤ Θ < 2π. However, any other interval of length 2π, for example – π < Θ ≤ π, can be such an interval.We shall take the value of θ such that – π < Θ ≤ π, called principal argument of z and is denoted by arg z, unless specified otherwise.