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I get different results for (1-i)^500 when solving it using an online complex numbers calculator and when solving it using MatLab. MatLab says it's supposed to be -1.809E75 with the imaginary part being zero. However, complex number calculation sites and the z^n = r^n(cos(nθ) + isin(nθ)) say it's -1.809E75 - (7.269E61)i. MatLab is known to be pretty reliable, and -7.269E61 seems extrodinarily big for an imaginary part but it's what the formula and some websites state. I wanted to know which one was right. Thank you.

talldude1998
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1 Answers1

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$(1-i)^2=-2i$, $(1-i)^4=-4$, \begin{align} (1-i)^{500}&=((1-i)^4)^{125}=-2^{250}\\ &=-1809251394333065553493296640760748560207343510400633813116524750123642650624\\ &\approx-1.809251394\times10^{75}. \end{align}

The imaginary part is zero, as predicted by de Moivre's formula.

Angina Seng
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