How Do You Solve the Complex Equation \( z^2 + 4\overline{z} + 4 = 0 \)?

[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

 

[Office_Shredder]

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

 

[ronho1234]

so is the answer just 2i^2?

 

[ronho1234]

or is it 2?

 

[jackmell]

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

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.