(-2+2i)(8+i)=0

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Solution for (-2+2i)(8+i)=0 equation: 


Simplifying
(-2 + 2i)(8 + i) = 0

Multiply (-2 + 2i) * (8 + i)
(-2(8 + i) + 2i * (8 + i)) = 0
((8 * -2 + i * -2) + 2i * (8 + i)) = 0
((-16 + -2i) + 2i * (8 + i)) = 0
(-16 + -2i + (8 * 2i + i * 2i)) = 0
(-16 + -2i + (16i + 2i2)) = 0

Combine like terms: -2i + 16i = 14i
(-16 + 14i + 2i2) = 0

Solving
-16 + 14i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 7i + i2) = 0

Factor a trinomial.
2((-8 + -1i)(1 + -1i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -1i)' equal to zero and attempt to solve:

Simplifying
-8 + -1i = 0

Solving
-8 + -1i = 0

Move all terms containing i to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1i = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1i = 0 + 8
-1i = 0 + 8

Combine like terms: 0 + 8 = 8
-1i = 8

Divide each side by '-1'.
i = -8

Simplifying
i = -8

Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1i = 0 + -1
-1i = 0 + -1

Combine like terms: 0 + -1 = -1
-1i = -1

Divide each side by '-1'.
i = 1

Simplifying
i = 1
Solution
i = {-8, 1}

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