## AmTran_Bus one year ago If z=1+i, then the magnitude of z is sqrt(2). What is the phase angle of z?

1. AmTran_Bus

Tan y/x. Book says 1, isnt it real/imag? How did they get that?

2. AmTran_Bus

I know they got the mag. by mult. by conjugate.

3. zepdrix

|dw:1441485844188:dw|

4. zepdrix

Just set up a triangle I guess :)

5. zepdrix

|dw:1441485936796:dw|

6. AmTran_Bus

Hum. Ok. The book just says use y/x (pchem book). If z=x+iy, and the mag is sqrt 2, can you not just say y/x?

7. AmTran_Bus

It says =1 which in angle terms is 45.

8. zepdrix

Yes, but I thought you were having trouble with it conceptually :P so i went into a little more detail lol

9. AmTran_Bus

Thanks for that! I actually understand the graph! Been doing Pchem all day and brain fried.

10. zepdrix

|dw:1441486086282:dw|

11. zepdrix

Therefore: $$\large\rm arctan\left(\frac{y}{x}\right)=\theta$$

12. zepdrix

Ya I guess we gotta be careful with our y, right? We're thinking of our complex number $$\large\rm z=x+iy$$ So the i is not included in the y. It's just the distance in that direction. So ya y=1, good good

13. AmTran_Bus

arctan (1/1) does not give 45 degrees though.

14. zepdrix

no? :o it should. are you in radians, maybe it's spitting out pi/4 as a decimal value

15. AmTran_Bus

Bless you, Zepdrix.

16. zepdrix

silly bus -_- we're gonna downgrade you to a shortbus some day

17. AmTran_Bus

I need to be.

18. zepdrix

XD