Editing Imaginary unit (section)

=== Quarter-turn rotation ===

When multiplied by the imaginary unit {{mvar|i}}, any arbitrary complex number in the complex plane is rotated by a quarter turn {{nobr|(<math>\tfrac12\pi</math> radians}} or {{math|90°}}) [[anticlockwise]]. When multiplied by {{math|−''i''}}, any arbitrary complex number is rotated by a quarter turn clockwise. In polar form:

<math display=block>i \, re^{\varphi i} = re^{(\varphi + \pi/2)i}, \quad
        -i \, re^{\varphi i} = re^{(\varphi - \pi/2)i}.</math>

In rectangular form,

<math display=block> i(a + bi) = -b + ai, \quad -i(a + bi) = b - ai.</math>