This episode is concerned with the field of complex numbers. In fact, we shall motivate the emergence of `imaginary numbers’ — particularly their prototype representative i — via entirely nothing really imaginary. Representing numbers as such as geometric operations we shall see that the number i can be interpreted as an operation on the plane. Indeed, in order to solve the equation x times x equals negative 1 for x, we look at the -1 as point reflection through the origin, which is the same as rotation by 180 degrees. Hence, two rotations by 90 degrees yield the point reflection and, thus, a solution x for the equation in question.

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