FP2 Complex number magnitude and argument

z = -j * e^(jx) * sin(x)

how do you possibly find the magnitude and argument of that?

Express e^(jx) as $\cos x + j\sin x$ and then you'll get it in the form $z = a+ bj$.

Thanks got it

$w=-je^{j\Theta}sin(\Theta)\\w=-j(cos(\Theta) + jsin(\Theta))sin\Theta\\w=-j(cos(\Theta)sin(\Theta)+jsin^2(\Theta))\\w=-jcos(\Theta)sin(\Theta)+sin^2(\Theta)\\|w| = \sqrt{(sin^2(\Theta))^2 + (cos(\Theta)sin(\Theta))^2}\\|w| = \sqrt{sin^4(\Theta) + cos^2(\Theta)sin^2(\Theta)}\\|w| = \sqrt{sin^2\Theta(sin^2(\Theta)+cos^2(\Theta))}\\|w| = sin(\Theta)\\$

Perfect!

The question does ask to find arg(w) too but i'm getting that wrong.

w =sin^2(x)-jcos(x)sin(x)

tan(x) = O/A = cos(x)sin(x)/sin^2(x)
tan(x) = cos(x)/sin(x)
tan(x) = 1/tan(x)
tan^2(x) = 1
tan(x) = +- 1
x = -pi/4 or pi/4

so x = -pi/4 but text book answer is theta - pi/2