One simple question please help!!

Question

z = i and w = -2 + 2i

arg(z) = ? π

arg(w) = ? π

Answer 1

The complex number z = i

It can be written as 0 + i

Compare it to complex number  x + i y

x = 0, y = 1

In this case x = 0, y > 0

Since x = 0, y > 0 use the formula b = tan^-1(y/x)

θ = tan^-1 (1/0)

θ = tan^-1 (∞)

θ =  π/2

Arg(z) = π/2.

Answer 2

The complex number w = - 2 + 2i

Compare it to x + iy

x = - 2 , y = 2

Since x < 0, use the formula for the argument

 θ = tan^-1(y/x) + 180^o

θ = tan^-1(2/-2) + 180^o

θ = tan^-1(-1) + 180^o

θ = - 45 + 180^o

θ = - π/4 + π

θ = 3π/4

Arg(w) = 3π/4.