Tricky complex numbers problem

[andrew.c]

Homework Statement

z1 = 1 + i, z2 = i − 5 are points in the complex plane. If z2 is rotated about z1 by 450
find its new position.

Attempt at solution
Absolutely no idea! I think I might need to use e^theta*i but not sure!

 

[dontdisturbmycircles]

What does that mean rotated about z1 by 450? Could you elaborate?

 

[andrew.c]

Sorry, that's all that was given...
I think it means like rotating 45 degs through the imaginary axis?

 

[dontdisturbmycircles]

But then what does that have to do with Z1.

 

[Dick]

45 degrees is pi/4 radians. To rotate around another point, find the difference z2-z1 and rotate that by pi/4 (sure, multiply by e^(i*pi/4)). Add the result back to z1.

 

[andrew.c]

thank you!