# complex roots

1. MrShorty

In working with complex numbers, I have observed that Excel stores complex numbers as text strings (even when they end up being real), which makes it difficult to apply number formatting.
2. MrShorty
Adding a note here for my future reference. Sometimes the problem being expressed is to find the rational powers of a negative number. One general approach to this (based on Euler's formula):

1) From Euler's formula, the solutions to the problem can be expressed as complex numbers of the form r*(cos(t+2*n*pi/d)+i*sin(t+2*n*pi/d)) where r is the abs value of the solution, t is the angle/argument of one solution, d is the denominator of the rational exponent, and n represent integers 0, ±1, ±2, ...
2) The n=0 solution is returned by the IMPOWER() function
3) use the IMABS() and IMARGUMENT() functions to get r and t.
4) Substitute other values for n to get other values for the complex solutions.
5) To find the real solutions (if any), find the values for n where t+2*n*pi/d is equal to 0 or pi (or 2*pi or 3*pi or ±k*pi). Remember: n must be an integer.
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