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# FP2 Complex number magnitude and argument

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

how do you possibly find the magnitude and argument of that?
2. (Original post by Bealzibub)
z = -j * e^(jx) * sin(x)

how do you possibly find the magnitude and argument of that?
Express e^(jx) as and then you'll get it in the form .
3. (Original post by Zacken)
Express e^(jx) as and then you'll get it in the form .
Thanks got it

4. (Original post by Bealzibub)
Thanks got it

Perfect!
5. (Original post by Zacken)
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
6. (Original post by Bealzibub)
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
This is what happens when you use/confuse the same variables. The argument is not x, so why are you writing tan x = f(x).Let's call the argument , then:

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