Answer: Option D.
Step-by-step explanation:
When we want to graph a complex number in a coordinate axis, the real part of the complex number is represented by the x-axis, and the complex part is represented by the y-axis.
in this case, we can see that the coordinates of the point are:
(-2, 2)
Then the complex number is:
Z = -2 + 2*i
Now we need to see which one of the given options is equal to this.
Let's check the real part for every option, so we can discard some of them:
A) real part = -2*cos(135°) = 1.41 (we can discard this option)
B) real part = 2*cos(7*pi/4) = 1.41 (we can discard this option)
C) real part = √2*2*cos(225°) = -2
D) real part = √2*2*cos(3*pi/4) = -2
So options C or D are the correct one, now let's check the complex part for each one
C) complex part = √2*2*sin(225°) = -2 (we can discard this option)
D) complex part = √2*2*sin(3*pi/4) = 2
So the correct one is the D option.
