complex equation

[squaremeplz]

1. The problem statement, all variables and given/known data

hi

in trying to solve 4z - 2conj(z) + i = 0



2. Relevant equations



3. The attempt at a solution

the calculator spits out z = -1/2*i

i did 4(a+bi) - 2(a - bi) + i = 0

4a + 4bi - 2a + 2bi + i = 0

2a + 6bi + i = 0

i get z = -1/6*i

did i mess up somewhere? also, are there other solutions?

Thanks!

[Dick]

You are right. The calculator is wrong. It looks like it solved 4z-2z+i=0.

[Mark44]

Oftentimes it's difficult to get a solution, but simple to check. If z = -i/6, then
4z - 2\bar{z} + i
4(-i/6) -2(i/6) + i = 0
This shows that z = -i/6 is the solution to your equation. Similarly, you can show that what the calculator produced is not the solution.