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The expression is $(a - j \mu_1 b) \div (z - \sqrt{z^2 - a^2 - \mu_1^2 b^2})$

$z = a$, the above expression reduces to $(a - j \mu_1 b) \div (a - \sqrt{- \mu_1^2 b^2})$

One way to refactor the above expression is using $j^2 = -1$, the above expression becomes $(a - j \mu_1 b)\div(a - j \mu_1 b)$, which should be 1 for any value of $\mu_1$...

But when I evaluate numerically using Python (cmath.sqrt()), I get 1 for $\mu_1 = 1, 2, 3....$ but not for $\mu_1 = 2+2j$ or any other complex number.

Ethan Chan
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user3873617
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1 Answers1

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First you have to clarify what you mean by sqrt, what Python thinks sqrt means, and whether you agree with Python or not. Every (nonzero) complex number has two square roots, and, unlike in the real case, you can't just say "take the positive one". Once you've done that, you'll find that some properties of sqrt that hold over real numbers don't hold over the complex numbers, so some manipulations you're doing aren't actually valid.

Ted
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