complex roots

  1. MrShorty
    For a first entry in this group, I decided to respond in more detail to a thread made in late May/Early June, asking how to get complex roots to a quadratic equation. Excel has several built in functions for working with complex numbers (usually IMxxx() functions such IMSUM() for adding, IMSQRT() for taking the sqrt of complex numbers, etc. See help files for complete list). I put together a relatively quick spreadsheet and, since the groups don't seem to allow uploading of spreadsheets into the posts, I put it in this group's pictures area (which seems to work. Let me know if you are able to download the file from there and see it).

    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.
Results 1 to 2 of 2

Search Engine Friendly URLs by vBSEO 3.6.0 RC 1