(2z - 4)² + 12 = 4

(2z - 4)² = -8

Take the square root of both sides

2z - 4 = 2i√2

2z = 4 +- 2i√2

Divide both sides by 2

z = 2 +- i√2

ANSWER

z = 2 + i√2, 2 - i√2

(2z – 4)2 + 12 = 4?

(2z-4)^2 = -8 = [(2(2)^(1/2)*i]^2 :where i^2 = -1

Square root both sides:

2z-4 = 2 * 2^(1/2) * i

2z = 4 + 2*2^(1/2)*i = 2[2+2^(1/2)*i]

z = 2+2^(1/2)*i] or

z = 2+i * 2^(1/2) <= ans

(2z – 4)2 + 12 = 4?

(2z -4)^2 = 4 - 12

(2z-4)^2 = -8

(2z - 4)^2 = 8 i^2

2 z - 4 = sqrt (8) i & 2 z - 4 = - sqrt (8) i

2 z = 4 + sqrt (8) i & 2 z = 4 - sqrt (8) i

z = 1 / 2 ( 2 sqrt (2) i + 4) & z = 1 / 2 ( 4 - 2 sqrt (2) i )

= 2 + sqrt (2) i & = 2 - sqrt (2) i

so,

(x-2- sqrt (2) i) ( x - 2 + sqrt (2) i) = 0

4z-16+12=4

4z=8

z=2