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What is the common log of complex number?

Updated: 8/17/2019
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15y ago

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We can define logab = (log b)/(log a)as would would for real numbers, just now the result depends on the branch of log defined at a and b.

Defining log is a little complicated. But Log (with a capital) can be defined as

Log z: = ln r + iθ = ln | z | + iArg z.

So Log10b = (Log b)/(Log 10) = (ln | z | + iArg z)/(Log 10)

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Q: What is the common log of complex number?
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