MHB Square Root Solutions for Complex Numbers

Thread starter Milly
Start date Apr 17, 2015
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Roots Square

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The discussion focuses on finding square roots of complex numbers, specifically addressing part (ii) of a problem. A participant mentions obtaining the result 3$e^{\frac{1}{6}\theta i}$, prompting clarification on whether it should be 3$e^{\frac{1}{6}\pi i}$. The correct square roots of a complex number in polar form are identified as $\sqrt re^{\frac12\theta i}$ and $\sqrt re^{(\frac12\theta + \pi) i}$. This highlights the importance of accurately applying the polar representation of complex numbers in calculations. The conversation emphasizes the nuances in determining square roots of complex expressions.

Apr 17, 2015

Milly

View attachment 4273Helppp for part (ii). I got 3$e^{\frac{1}{6}\theta i}$

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Apr 17, 2015

Opalg

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MHB

Milly said:

Helppp for part (ii). I got 3$e^{\frac{1}{6}\theta i}$ Do you mean $\color{red}{3e^{\frac{1}{6}\pi i}}$?

The two square roots of $re^{\theta i}$ are $\sqrt re^{\frac12\theta i}$ and $\sqrt re^{(\frac12\theta+ \pi) i}$.

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