what quadrant is the complex number 32i inSolutionSolution H

what quadrant is the complex number -3-2i in?

Solution:

Here;

z= -3-2i = x+yi = r(cos + i sin)

As we know;

Re(z) = real part of z = -3 = rcos

Im(z) = imaginary part of z = -2 = rsin

=> tan = rsin / rcos

=> tan = -3 / -2

=> = tan^-1(3/2)

=> = 56.31^o

but as the values x<0 and y<0

=> Arg(z) =Argument of the complex number = - +

=> Arg(z) = -180^o + 56.31^o

=> Arg(z) = -123.69^o (Third quadrant)