1- Find the two square roots of the complex number z=3+4i.
2a- Solve in ℂ the equations: (E): 4z^2-10iz-7-i=0
b- Let a and b be solutions to (E) such that: Re(a)<0 and the two points A and B plots/pictures of a and b. Show that b/a=1-i. Conclude that AOB is an equilateral triangle.
The Attempt at a Solution
1- After solving (p+qi)^2=3+4i i found that the solutions were either 2+i or -2-i.
2-a For the complex equation i found two complex roots: z1=(-3+6i)/8 and z2=(3+14i)/8.
b- So i took the two solutions that i found from the previous question and chose a=z1 and b=z2 and after computing i got a whole different answer. Is my work correct, if not some help would be very much appreciated.