Question
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.
Solution:
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.
Solution:
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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