Factorzing polynomials with complex coefficients

[FelixHelix]

Not sure if this is the right place to post (but its related to a complex analysis questions)

I'm doing a past paper for my revision and am stuck at the first hurdle. I simply cannot factor this polynomial in z for the life of me. I've tried completing the square and the usual quadratic formula but do not get the answer as given.

I know what the answers are supposed to be so if anyone could help walk me through how you get there and if there is a technique of generally doing so I'd be most grateful.

$$z^2-(2i+4)z + 8i = (z-4)(z+2i)$$

 

[Office_Shredder]

Why don't you show us how you tried doing the quadratic formula? Because it should work

 

[FelixHelix]

I can:

$$z1,z2= \frac{(2i+4) \pm \sqrt{(2i+4)^2-(4)(1)(8i)}}{(2)(1)}$$
this simplifies to:
$$z1,z2 = (i+2) \pm \sqrt{3-4i}$$

Which isn't what I need...

Do you get the solutions z = 4 and z = 2i?

 

[Office_Shredder]

You did get those numbers. Do you know what the square root of 3-4i is?

 

[FelixHelix]

Hi Shredder - No I didn't know how to take the sqrt of a complex number... but I do now. Thanks for pointing this out - I looked it up and am happy with dealing with these now. Your help is much appreciated!

Felix