A-level: further mathematics: complex numbers

Does anyone know how to answer the following questions :
1)The two square roots of the complex number -7 + 24i are
A + Bi and C + Di, where A>0 and B>0.
Find and input the values of A, B, C and D.
2)The equation (2+3i)z + 3 - i = iz - 1 has the solution z = A + Bi.
Find and input the values of A and B, giving your answers in their simplest form.
3)a) The complex number z = 2 - 3i is represented on an Argand diagram. What would be its equivalent coordinates? (Input with no spaces please)
b) |z| can be written in the form √A where A is an integer. Input A.
c) Find zz*
4. The solutions of the quadratic equation z2 - 6z + 13 = 0 are
z1 = A + Bi and z2 = C + Di, where A>0, B>0.
Input A, B, C and D.
5. a) Re( 1+ 4i + (2-3i)/(2+i) ) = A/B , where A, B are integers. Input A, B.
b) Im( (3+i)/(2+5i) - (3-i)/(2-5i) ) = C/D where C,D are integers, D>0.
Input C,D.
6. Show that Im (√(2i) + √(-2i)) can have three possible values A, B, C where A>B>C. Input A,B,C.

I am very stuck on these and don't really know what to do so if anyone knows how to work these out telling or showing me would be very appreciated . Thank you .

OkY so start with question 1: what have you tried, what are your thoughts on how to begin?
To begin I started by labelling -7+24i as a+bi squared .begin I started by labelling -7+24i as a+bi squared . Than I expanded that to give me a^2 +2bai-b^2 = -7+24i . Then I collected the real parts and the imaginary parts so that a^2-b^2=-7 and 2bai= 24i . the I took the imaginary part and decide through by i to give me 2ba=24 and then I divided by 2b to make a the subject which got me to 12/b . Then I substituted a into the real part of the equation so then I had (12/b)^2 +b^2=-7 so 144/b^2 +b^2 = -7 . Times it all by b^2 to give me b^4 -7b^2 -144 =0 . The I said that c=b^2 so that c^2 -7c -144 =0 . Then I factorised (c-16)(c+9) giving me c= 16 c=-9 . And I square rooted this to give me b , b=4 b= square root of -9 or 3i . So I put this back into the equation which meant a =3 or and I could work the other a out as I didn’t know how to sub in 3i into the equation . Also thank you for the help in advance .

Than I expanded that to give me a^2 +2bai-b^2 = -7+24i . Then I collected the real parts and the imaginary parts so that a^2-b^2=-7 and 2bai= 24i . the I took the imaginary part and decide through by i to give me 2ba=24 and then I divided by 2b to make a the subject which got me to 12/b . Then I substituted a into the real part of the equation so then I had (12/b)^2 +b^2=-7 so 144/b^2 +b^2 = -7 . Times it all by b^2 to give me b^4 -7b^2 -144 =0 . The I said that c=b^2 so that c^2 -7c -144 =0 . Then I factorised (c-16)(c+9) giving me c= 16 c=-9 . And I square rooted this to give me b , b=4 b= square root of -9 or 3i . So I put this back into the equation which meant a =3 or and I could work the other a out as I didn’t know how to sub in 3i into the equation . Also thank you for the help in advance .

Than I expanded that to give me a^2 +2bai-b^2 = -7+24i . Then I collected the real parts and the imaginary parts so that a^2-b^2=-7 and 2bai= 24i . the I took the imaginary part and decide through by i to give me 2ba=24 and then I divided by 2b to make a the subject which got me to 12/b . Then I substituted a into the real part of the equation so then I had (12/b)^2 +b^2=-7 so 144/b^2 +b^2 = -7 . Times it all by b^2 to give me b^4 -7b^2 -144 =0 . The I said that c=b^2 so that c^2 -7c -144 =0 . Then I factorised (c-16)(c+9) giving me c= 16 c=-9 . And I square rooted this to give me b , b=4 b= square root of -9 or 3i . So I put this back into the equation which meant a =3 or and I could work the other a out as I didn’t know how to sub in 3i into the equation . Also thank you for the help in advance .

I think you've basically done it! The question should really state that A, B, C and D are real numbers, although the conditions A > 0 and B > 0 imply that they have to be real.

Note that if X^2 = Z then (-X)^2 = Z also, so if you have generated one root with positive values of A and B then you can derive the other root immediately.

Thank you for the help !
Do you have any idea on how to work out 2 , 5 and 6 as I really don’t even know where to start with those ?