3)
(2i)x^2 + x + 3i = 0 factor out the 2i
2i ( x^2 + (1/2i)x + 3/2) = 0 divide both sides by 2i
x^2 + (1/2i)x + 3/2 = 0
x^2 + (1/(2i))x = - 3/2 complete the square on x
Take (1/2) of (1 /(2i)) = (1/(4i))
Square this = (1/(4i)) (1/ (4i)) = 1/(16i^2) = 1/ -16 = -1/16
Add this to both sides
x^2 + (1/(2i))x - 1/16 = -3/2 - 1/16 factor the left.....simplify the right
(x + (1/(4i))^2 = -25/16 take both roots
x + (1/(4i) ) = ±(5/4)i subtract (1/(4i)) from both sides
x = ±(5/4)i - (1/(4i)) multiply top/bottom of the last fraction by i
x = ±(5/4)i - i / (4i^2)
x = ±(5/4)i - (i / (-4) )
x = ±(5/4)i + i/4
x = ±(5/4)i + (1/4)i
x = ±(5/4)i + (1/4)i
x = (5/4)i - (1/4) i = (4/4)i = i
or
x = (-5/4)i - (1/4)i = (-6/4)i = (-3/2)i
So.....the solutions are
x = (-3/2)i and x = i