The laws of exponents hold for complex numbers a and b: za z b z ab , z a z b z ab , (z
Chapter 17, Problem 48(choose chapter or problem)
The laws of exponents hold for complex numbers \(\alpha\) and \(\mathcal{B}\):
\(z^{\alpha} z^{\beta}=z^{\alpha+\beta}\), \(\frac{z^{\alpha}}{z^{\beta}}=z^{\alpha-\beta}\), \(\left(z^{\alpha}\right)^{n}=z^{n \alpha}\), n an integer.
However, the last law is not valid if n is a complex number. Verify that \(\left(i^{i}\right)^{2}=i^{2 i}\), but \(\\left(i^{2}\right)^{i} \neq i^{2 i}\).
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