The complex reciprocal function 1/z

Drag the blue points to see the effect of inverting the complex number z. The checkboxes show different shapes. The "before" shape is filled in, and is traced by the blue point P. The "after" shape is not filled, and is traced by P'.

This function finds the reciprocal, or multiplicative inverse, of a complex number z=x+iy. This can be done algebraically by "rationalizing the denominator": write 1/z as a fraction, then multiply top and bottom by x-iy and simplify.

The absolute value of 1/z is 1 over the absolute value of z.
The angle of 1/z is the negative of the angle of z.

Susan Addington, Created with GeoGebra

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