Q26 of 66 Page 91

State True of False for the following:

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

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.


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