Interpreting the hour hand on a clock as a two-dimensional object on a plane, the hand’s tip can be seen as a complex number.

This clock converts the hour hand’s position into a complex number, sets the number’s length to the current minutes and displays it in the form .

The angle is determined by the hours passed () but has to be slightly modified because a complex number starts at the horizontal axis and turns anti-clockwise whilst an hour hand starts at the vertical axis and turns — as the name implies — clockwise.

Thus .

The complex number’s length is simply determined by the minutes passed. Because the length must not be equal to , I simply add 1. .

Lastly, to convert a complex number in the form into the form , I use the formula .

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# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 29th of July, 2016
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