Complex numbers (1 Viewer)

[YBK]

Hey, just a complex number question:

If |z| = r and arg z = theta

show that z/(z^2+r^2) is real and give its value.


I used z = x+iy

and the answer I got was 1/2x
now x is the cos value

therefore

1/2cos theta is the answer. But the answer at the back of the book is 1/2rcos theta

Can anyone please explain this...

Thanks

 

[Riviet]

Since |z|=r and arg(z)=theta
z=rcis(theta)=rcos(theta)+risin(theta)
Since you let z=x+iy,
1/2x=1/2Re(z)
=1/2rcos(theta), since rcos(theta) is the real part of z (the bit I underlined before).
I hope that explains things.

 

[YBK]

Since |z|=r and arg(z)=theta
z=rcis(theta)=rcos(theta)+risin(theta))
Since you let z=x+iy,
1/2x=1/2Re(z)
=1/2rcos(theta), since rcos(theta) is the real part of z (the bit I underlined before).
I hope that explains things.

yay! I understand perfectly now!
thank you