we have two responses for you

Hi Ash,

I didn't see how to factor this so I decided to try the general quadratic. This involves the root of b² - 4ac which I calculated to be

b² - 4ac = (6 + 2i)² - 4 (8 + 61) = 36 + 24i -4 - 32 - 24i = 0.

so the only solution is -b/2a = (6 +2 i)/2 = 3 + i.

Now that you know the answer it's easy to check. Expand [z - (3 + i)]² and check that you get
z² - (6+2i)z + (8+6i)

Penny

Hi Ash.

Try completing the square by taking the c term to the other side and using half the b term:

You have z² + bz + c = 0, so to complete the square ( z + b/2 )² = -c + (b/2)².

Thus [ z - (3+i) ]² = - (8+6i) + (3 + i)²

Solve for z.

Stephen La Rocque.