Question

Please help me please help me

Answer 1

U'(-2 , -2)

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

`z^(\prime )=e^{i(3\pi )/(2) }* z`

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)