(-7+8i)(-2+4i)=

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Solution for (-7+8i)(-2+4i)= equation: 


Simplifying
(-7 + 8i)(-2 + 4i) = 0

Multiply (-7 + 8i) * (-2 + 4i)
(-7(-2 + 4i) + 8i * (-2 + 4i)) = 0
((-2 * -7 + 4i * -7) + 8i * (-2 + 4i)) = 0
((14 + -28i) + 8i * (-2 + 4i)) = 0
(14 + -28i + (-2 * 8i + 4i * 8i)) = 0
(14 + -28i + (-16i + 32i2)) = 0

Combine like terms: -28i + -16i = -44i
(14 + -44i + 32i2) = 0

Solving
14 + -44i + 32i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -22i + 16i2) = 0

Factor a trinomial.
2((1 + -2i)(7 + -8i)) = 0

Ignore the factor 2.

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

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5

Subproblem 2
Set the factor '(7 + -8i)' equal to zero and attempt to solve:

Simplifying
7 + -8i = 0

Solving
7 + -8i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8i = 0 + -7
-8i = 0 + -7

Combine like terms: 0 + -7 = -7
-8i = -7

Divide each side by '-8'.
i = 0.875

Simplifying
i = 0.875
Solution
i = {0.5, 0.875}

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