In the complex plane, multiplying a given function by i rotates it anti-clockwise by how many degrees?

The story behind the answer

Multiplying a complex number by i rotates it 90° anticlockwise. That’s because i = cos 90° + i sin 90° = e^{iπ/2}, so it represents a pure quarter-turn on the complex plane. Algebraically, if z = x + iy, then iz = -y + ix, which maps the point (x, y) to (-y, x)—exactly a 90° counterclockwise rotation.

Context tip: In general, multiplying by re^{iθ} scales by r and rotates by θ. Since |i| = 1, it only rotates. Memory trick: powers