Question

how do i plot this points on the unit circle?
(-sqrt2)+(sqrt2 i)
(-3/2)+(3/2) (sqrt3i)
2-2 (sqrt3i)
(-5sqrt2/2) - (5isqrt2/2

Answer 1

Suppose the first number is called z.
Then Re(z) = -sqrt(2) and Im(z) = sqrt(2).

Also |z|=sqrt((Re(z))²+(Im(z))²)=sqrt(2+2)=sqrt(4)=2.
So z does not lie on the unit circle, it is 2 units from the origin...

It can be plotted on a circle with radius 2.
Where? Look at Re(z) and Im(z). To get to z, you have to go to the left and then the SAME step up! This means z lies on the line y=-x. If you draw this line, the intersection point with the circle in the 2nd quadrant is z.

The other numbers are dealt with in the same way (also not on the unit circle...)

Answer 2

In this image I've drawn the first one...