a)Find (in rectangular form) the two values of sqrt(8+6i)
b)Solve the equation z^2 +sqrt(32)iz6i=0.
Thanks for your help
b)Solve the equation z^2 +sqrt(32)iz6i=0.
Thanks for your help

a) 8 + 6i = 9 + 1 + 6i = 1*9 + 1 + 6i = 9i^2 + 6i + 1 = (3i + 1) ^2 or (3i  1)^2.
The two roots are 1 + 3i and 1  3i.
b) z^2 + [i * sqrt(32)] z + (6i) = 0
Use Quadratic Formula:
a = 1, b = [i * sqrt(32)], c = (6i)
z = { [i * sqrt(32)] + or  sqrt(32 + 24i) } / 4
z = { [i * sqrt(32)] + or  [2 * sqrt(8 + 6i)] } / 4
z = { [i * sqrt(32)] + or  [2 * (1 + 3i)] } / 4
z = [i * 4 * sqrt(2) / 4] + or  (1 + 3i)/2
z = sqrt(2) * i + 1/2 + 3 * i or sqrt(2) * i  1/2  3 * i
z = 1/2 + (3  sqrt(2)) * i or 1/2 + (3  sqrt(2)) * i
The two roots are 1 + 3i and 1  3i.
b) z^2 + [i * sqrt(32)] z + (6i) = 0
Use Quadratic Formula:
a = 1, b = [i * sqrt(32)], c = (6i)
z = { [i * sqrt(32)] + or  sqrt(32 + 24i) } / 4
z = { [i * sqrt(32)] + or  [2 * sqrt(8 + 6i)] } / 4
z = { [i * sqrt(32)] + or  [2 * (1 + 3i)] } / 4
z = [i * 4 * sqrt(2) / 4] + or  (1 + 3i)/2
z = sqrt(2) * i + 1/2 + 3 * i or sqrt(2) * i  1/2  3 * i
z = 1/2 + (3  sqrt(2)) * i or 1/2 + (3  sqrt(2)) * i

Asia O`_`O