## Coursera: analysis complex kind Week 3.3. Complex exponential function.

### Jul 18, 2016

### Background:

Hence,

Overall:

### Definition

f(z) = =

When y = 0, this is same as real exponential function

Properties

(since sits on the unit circle, thus has size = 1)

Also,

from above, is the modulus or size of radius of , then is in polar form and hence y is argument of

Note: (from earlier lecture – ref required) is not used in determining and do not confuse this with

by setting z = x+iy and w= u + iv

, since

modulus (length) = 1 so x =0, and argument =

Hence , when then therefore z – w =

So z = w + results in

<< to be done : mapping w = >>

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Jul 26, 2016 at 6:35 pm

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