can someone please show me how

exp(.5ln(3e^(i*theta))

is

exp(.5(ln3+i*theta))

i thought e^(ab) was not equal to e^a times e^b

rather e^(a+b) was e^a times e^b

thnks

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- Feb 18th 2010, 03:59 PM #1

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- Feb 18th 2010, 06:20 PM #2

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It's just the definition of the complex natural logarithm $\displaystyle Ln\,z$ , with $\displaystyle \ln|z|$ the usual real natural logarithm:

for $\displaystyle z\in\mathbb{C}\,,\,\,Ln\, z:=\ln|z|+i\arg(z)$ , so:

$\displaystyle Ln\left(3e^{i\theta}\right)=\ln 3+i\theta$ ...

Tonio

- Feb 18th 2010, 07:20 PM #3

- Feb 19th 2010, 03:25 AM #4

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