SOLUTION: If z1 and z2 are two complex numbers with |z1|=|z2| ,then which of the following are true. 1. Z1=z2 2 real part of z1=real part of z2 3.imaginary part of z1=imaginary part of z2

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: If z1 and z2 are two complex numbers with |z1|=|z2| ,then which of the following are true. 1. Z1=z2 2 real part of z1=real part of z2 3.imaginary part of z1=imaginary part of z2      Log On


   

Question 1074759: If z1 and z2 are two complex numbers with |z1|=|z2| ,then which of the following are true.
1. Z1=z2
2 real part of z1=real part of z2
3.imaginary part of z1=imaginary part of z2
Found 2 solutions by Edwin McCravy, Fombitz:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
None of those choices are correct.  Here is a counter-example:

z%5B1%5D+=+39%2B52i,  z%5B2%5D+=+25%2B60i


abs%28z%5B1%5D%29+=+sqrt%2839%5E2%2B52%5E2%29,  abs%28z%5B2%5D%29+=+sqrt%2825%5E2%2B60%5E2%29

abs%28z%5B1%5D%29+=+sqrt%281521%2B2704%29,  abs%28z%5B2%5D%29+=+sqrt%28625%2B3600%29

abs%28z%5B1%5D%29+=+sqrt%284225%29,  abs%28z%5B2%5D%29+=+sqrt%284225%29

abs%28z%5B1%5D%29+=+65,  abs%28z%5B2%5D%29+=+65

So  

abs%28z%5B1%5D%29+=+abs%28z%5B2%5D%29 is true.

However, they are not equal, their real parts are not equal,
and their imaginary parts are not equal.  So none of those
choices are true.  Be sure to point this out to your
teacher.

Edwin

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If z%5B1%5D=a%2Bbi and z%5B2%5D=c%2Bdi and
abs%28z%5B1%5D%29=abs%28z%5B2%5D%29
Then,
sqrt%28a%5E2%2Bb%5E2%29=sqrt%28c%5E2%2Bd%5E2%29
a%5E2%2Bb%5E2=c%5E2%2Bd%5E2
...
..
.
1. a=b and c=d, not necessarily
2. a=b, not necessarily
3. c=d, not necessarily