to change it to e I think you change it in the form of e^itheta = cos(theta)+isin(theta)
consider the complex function
f(z) = e ^(2z^(2)+2)
let f(x+iy)=u(x,y)+iv(x,y)
calculate u(x,y) and v(x,y)
after substituing z=x+iy I get
e^(2x^(2)-2y^(2)+2) . e^(4xiy)
how do i get rid of e.
if i have done it wrong then plz tell me whats the mistake.plz help
f(z) = e^(2z² + 2)
f(x + iy)
= e^(2(x + iy)² + 2)
= e^(2(x² + 2ixy + i²y²) + 2)
= e^(2(x² + 2ixy - y²) + 2)
= e^(2x² + 4ixy - 2y² + 2)
= e^(4ixy)e^(2x² - 2y² + 2)
= [cos(4xy) + isin(4xy)]e^(2x² - 2y² + 2)
= cos(4xy)e^(2x² - 2y² + 2) + isin(4xy)e^(2x² - 2y² + 2)
So:
u(x,y) = cos(4xy)e^(2x² - 2y² + 2)
v(x,y) = sin(4xy)e^(2x² - 2y² + 2)