# Complex Solutions

by Rubik
Tags: complex, solutions
 P: 97 1. The problem statement, all variables and given/known data Find all complex solutions to $\bar{z}$ = z 2. Relevant equations z = x + iy and $\bar{z}$ = x - iy 3. The attempt at a solution What does it mean by find all complex solutions? $\bar{z}$ = z 0 = x + iy - x + iy 0 = 2iy 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
 P: 16 Two complex numbers are only equal if their real parts are equal and their imaginary parts are equal so you may have to equate real and imaginary parts to find the values of x and y.
Emeritus
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PF Gold
P: 7,819
 Quote by Rubik 1. The problem statement, all variables and given/known data Find all complex solutions to $\bar{z}$ = z 2. Relevant equations z = x + iy and $\bar{z}$ = x - iy 3. The attempt at a solution What does it mean by find all complex solutions? $\bar{z}$ = z 0 = x + iy - x + iy 0 = 2iy
If 0 = 2iy, then ...
1. What must x be for this to be true?

2. What must y be for this to be true?

 P: 16 Complex Solutions 2y = 0 and x=0
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,564 How do you arrive at "x= 0" from an equation that does not have an "x" in it??
 P: 446 Well the basic form is x + iy, so we know the x part of the complex number must be equal to zero if it's not there.
Emeritus
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,564 Yes, and as you have been told repeatedly, that is wrong. The equation 2iy= 0 does NOT say "x= 0 because x isn't there". The fact that x is not in that equation means that the equation does not tell you anything about x. Suppose z= 4+ 0i. What is $\overline{z}$?