How do I Solve 4z - 2conj(z) + i = 0?

[squaremeplz]

Homework Statement

hi

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

Homework Equations

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.