BMAD 65 Posted November 16, 2018 Report Share Posted November 16, 2018 Write the complex form (a + bi) for: Sqrt ( i ) Quote Link to post Share on other sites

1 Solution EventHorizon 16 Posted November 16, 2018 Solution Report Share Posted November 16, 2018 Spoiler .5*sqrt(2) + .5*sqrt(2)*i or -.5*sqrt(2) - .5*sqrt(2)*i An interesting thing I was shown was that, if you look at the complex plane, multiplying two complex numbers results in adding the angles and multiplying the magnitudes of the vectors representing the complex numbers being multiplied. This makes finding an nth root of complex numbers fairly simple. Simply take the nth root of the magnitude, and divide the angle by n. Then you just calculate the real and imaginary parts from the resulting vector using sine and cosine. Finding all the other values for the nth roots is done by simply adding 2pi/n repeatedly to the angle of any found nth roots. Quote Link to post Share on other sites

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## BMAD 65

Write the complex form (a + bi) for:

Sqrt ( i )

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