Graphical representation of complex numbers

[g117]

Hi there,

eI have two numbers:

z1 = 2 + i
z2 = exp(iδ) * z1

i are complex numbers and δ is a real number. I need to answer a question - what does the graphical representation of z2 have in relation to the graphical representation of z1.

Thanks for any help!

 

[dx]

Multiplying by exp(ia) is a rotation by the angle a.

This looks like a homework question. We have a special forum for that here, so in future post such questions there, and also try to tell us a little about how you've attempted to solve it, so that the help you receive is more meaningful.

 

[g117]

Thanks a lot.

I'm sorry for posting in wrong section. I'm totally new on this forum. And yes, it is a homework question. Of course, I tried to solve it myself, but the only thing I know is, that:

e^(iδ) = cos δ + i sin δ

And I would also like to know, what's the reason - why is it a rotation.

 

[dx]

If you rotate a vector (x, y) by an angle θ, the components x' and y' of the rotated vector are

x' = xcosθ - ysinθ
y' = xsinθ + ycosθ

Now a complex number z = x + iy is like a vector with components x and y. Multiply x + iy with exp(iθ) = cosθ + isinθ, and you will get x' + iy' with x' and y' as above.