How do i get the modulus of the root

Ok so im asked to solve the equation z^2-2iz-5=0 and express it in a form of x+iy.

The answers that i got are i+2 and i-2

How do i get the argument and modulus of the value?
is it i+2 multiplied by i-2? The answer i got was -5 for the modulus but the answer is root of 5. And how do i get the argument?

The solutions to said equation are correct. The modulus of a complex number x + iy is found by calculating the following value: √(x^2 + y^2). Assuming you are familiar with Argand diagrams, it is essentially using Pythagoras' theorem to find the length of the line representing the complex number. For both of our roots, we have √(2^2 + 1^2), which equals √5

The argument isn't that much harder. It's given by the formula θ=arctan(y/x). Again, going back to the Argand diagram, the argument is equal to the angle between the positive x axis and the line representing the complex number, measured in an anticlockwise sense. By drawing the two lines, we can see there is a right angled triangle, and we can use the formula: tanθ = y/x, or θ = arctan(y/x)
For 2+i, this equals arctan(1/2), which equals 0.46 radians, or 26.6 degrees.

for -2 + i, we get arctan(1/(-2)) = -0.46 radians or -26.6 degrees. However, care must be taken, as by looking at the Argand diagram representing this point, we can see that the answer is actually π-0.46, or 2.68 radians or 153.4 degrees

I hope this helps and isn't too verbose :D

z^2-2iz-5 = 0,
You have : (z-2-i)(z+2-ii) = 0,
OR,
z = 2 + i, &, z = -2 + i,
SO,
Argument = arctan(1/2) = 26.57°, >========================< ANSWER
& Agument = arctan(1/-2) = 180-26.57 = 153.43° >=============< ANSWER
AND
Modulus(IN BOTH) = sqrt[2^2+1^2] = sqrt(5) >====================< ANSWER