# Thread: prove this representation also work!

1. ## prove this representation also work!

if z = x + iy
prove:z = re^(iθ) also work

Also,prove: dz= e^(iθ) dr + ire^(iθ)dθ

2. ## Re: prove this representation also work!

Polar form of a complex number z = x + iy is
z = r[ cos(theta) + i sin(theta) ]
and cos(theta) + i sin(theta) = e^i(theta)

3. ## Re: prove this representation also work!

also,please prove : dz= e^(iθ) dr + ire^(iθ)dθ

4. ## Re: prove this representation also work!

again from polar for of z dz = [ cos(theta) + i sin(theta) ] dr + r [-sin(theta) + i cos(theta)] d(theta)

dz = [ cos(theta) + i sin(theta) ] dr + i r [ cos(theta) + i sin(theta)] d(theta) that gives required result

5. ## Re: prove this representation also work!

Originally Posted by waqarhaider
again from polar for of z dz = [ cos(theta) + i sin(theta) ] dr + r [-sin(theta) + i cos(theta)] d(theta)

dz = [ cos(theta) + i sin(theta) ] dr + i r [ cos(theta) + i sin(theta)] d(theta) that gives required result
May you put it in latex,please,i have little confused

6. ## Re: prove this representation also work!

Originally Posted by victorlui
May you put it in latex,please,i have little confused
What was posted is perfectly readable. The problem is, perhaps, you are out of your depth trying to understand things that depend on pre-requisite knowledge you do not currently have.