1. ## help with exp

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

2. Originally Posted by mpl06c
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

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

3. Originally Posted by mpl06c
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
Yes, but ln(ab)= ln(a)+ ln(b) and that is what is being used.

ln(3e^(i*theta))= ln(3)+ ln(e^(i*theta))= ln(3)+ i*theta.