(7+8i)(-4-6i)=

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Solution for (7+8i)(-4-6i)= equation: 


Simplifying
(7 + 8i)(-4 + -6i) = 0

Multiply (7 + 8i) * (-4 + -6i)
(7(-4 + -6i) + 8i * (-4 + -6i)) = 0
((-4 * 7 + -6i * 7) + 8i * (-4 + -6i)) = 0
((-28 + -42i) + 8i * (-4 + -6i)) = 0
(-28 + -42i + (-4 * 8i + -6i * 8i)) = 0
(-28 + -42i + (-32i + -48i2)) = 0

Combine like terms: -42i + -32i = -74i
(-28 + -74i + -48i2) = 0

Solving
-28 + -74i + -48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(14 + 37i + 24i2) = 0

Factor a trinomial.
-2((7 + 8i)(2 + 3i)) = 0

Ignore the factor -2.

Subproblem 1
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

Subproblem 2
Set the factor '(2 + 3i)' equal to zero and attempt to solve:

Simplifying
2 + 3i = 0

Solving
2 + 3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3i = 0 + -2
3i = 0 + -2

Combine like terms: 0 + -2 = -2
3i = -2

Divide each side by '3'.
i = -0.6666666667

Simplifying
i = -0.6666666667
Solution
i = {-0.875, -0.6666666667}

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