Question:
The multiplication of a non-zero complex number by i rotates it through ____________ in the anti-clockwise direction.
Solution:
Let z = x + iy then iz = ix + i2y
i.e iz = ix – y
i.e iz = – y + ix
$\tan \theta_{1}$ for $z=x+i y, \tan \theta_{1}=\frac{y}{x}$
$\tan \theta_{2}$ for $i z=i x-y, \tan \theta_{2}=\frac{x}{-y}$
Since $\tan \theta_{1} \times \tan \theta_{2}=\frac{y}{x} \times \frac{x}{-y}=-1$
i.e iz is rotated by $90^{\circ}$.
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