Answer:
U'(-2 , -2)
Step-by-step explanation:
U(2 , -2)
Let R be the rotation of center the origin O(0 , 0) and angle 270
Let M(z = x + iy) a point of the plane and its image M'(z' = x' + iy') by the rotation R.
Then
[tex]z^{\prime }=e^{i\frac{3\pi }{2} }\times z[/tex]
Then
x' + iy' = (0 -i)×(x + iy)
Then
x' + iy' = (-i) × (x + iy)
= -ix + y
Then
x' = y and y' = -x
Then
R transform M(x , y) to the point M'(y , -x)
Conclusion :
The image of U(2 , -2) by R is :
U'(-2 , -2)
