- #1
Milly
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View attachment 4273Helppp for part (ii). I got 3$e^{\frac{1}{6}\theta i}$
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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.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...