State True of False:Multiplication of a non zero complex number by –

1.	State True of False:Multiplication of a non zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.
Answer» False Explanation: Let z = x + iy, where x, y > 0 i.e. z or point A (x, y) lies in first quadrant. Now, -iz = -I (x + iy) = -ix – i²y = y – ix Now, point B (y, -x) lies in fourth quadrant. Also ∠AOB = 90° Thus, B is obtained by rotating A in clockwise direction about origin.

State True of False:Multiplication of a non zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.

Answer»

False

Explanation:

Let z = x + iy, where x, y > 0

i.e. z or point A (x, y) lies in first quadrant.

Now, -iz = -I (x + iy)

= -ix – i²y

= y – ix

Now, point B (y, -x) lies in fourth quadrant.

Also ∠AOB = 90°

Thus, B is obtained by rotating A in clockwise direction about origin.