1. Apr 22, 2012

### ronho1234

find all solutions to z^2+4z ̅+4=0 where z is a complex number. Please help with this qn i'm having difficulty. thanks

2. Apr 22, 2012

### Office_Shredder

Staff Emeritus
It's a quadratic polynomial. Do you not know how to factor these/the quadratic formula?

3. Apr 22, 2012

### ronho1234

so is the answer just 2i^2???

4. Apr 22, 2012

### ronho1234

or is it 2?

5. Apr 23, 2012

### jackmell

That's a conjugate isn't it?

Suppose so then you have:

$$z^2+4\overline{z}+4=0$$

Then let $z=a+bi$

so:

$$(a+bi)^2+4(a-bi)+4=0$$

equate real and imaginaries to zero. That's two equations in two unknowns. Solve them.