I need the proof for (e^z1)(e^z2)=e^(z1+z2)

using the power series expansion for e^z=1+z+(z^2)/2! + (z^3)/3! +....

I've tried it a couple of times but cant seem to get it.

thanks for any help!!

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- Sep 15th 2008, 04:40 PMgidget[SOLVED] Complex exponential proof
I need the proof for (e^z1)(e^z2)=e^(z1+z2)

using the power series expansion for e^z=1+z+(z^2)/2! + (z^3)/3! +....

I've tried it a couple of times but cant seem to get it.

thanks for any help!! - Sep 15th 2008, 04:46 PMicemanfan
is a result of one of the rules of exponents. It requires no proof, at least not if I'm teaching.

- Sep 15th 2008, 04:49 PMgidget
yeah i've proved it using exponent laws no problem but our prof said to do it the other way and wants it proved using the power series.

- Sep 15th 2008, 05:49 PMThePerfectHacker
- Sep 15th 2008, 06:25 PMSoroban
Hello, gidget!

Quote:

I need the proof for: .

using the power series expansion: .

We have: .

Multiply: .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Add down the columns . . .

.