Thread: prove this representation also work!

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

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

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)

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

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

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

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.