(5+4i)(-8-7i)=

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Solution for (5+4i)(-8-7i)= equation: 


Simplifying
(5 + 4i)(-8 + -7i) = 0

Multiply (5 + 4i) * (-8 + -7i)
(5(-8 + -7i) + 4i * (-8 + -7i)) = 0
((-8 * 5 + -7i * 5) + 4i * (-8 + -7i)) = 0
((-40 + -35i) + 4i * (-8 + -7i)) = 0
(-40 + -35i + (-8 * 4i + -7i * 4i)) = 0
(-40 + -35i + (-32i + -28i2)) = 0

Combine like terms: -35i + -32i = -67i
(-40 + -67i + -28i2) = 0

Solving
-40 + -67i + -28i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(40 + 67i + 28i2) = 0

Factor a trinomial.
-1((5 + 4i)(8 + 7i)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 4i)' equal to zero and attempt to solve:

Simplifying
5 + 4i = 0

Solving
5 + 4i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4i = 0 + -5
4i = 0 + -5

Combine like terms: 0 + -5 = -5
4i = -5

Divide each side by '4'.
i = -1.25

Simplifying
i = -1.25

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

Simplifying
8 + 7i = 0

Solving
8 + 7i = 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 + 7i = 0 + -8

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

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

Divide each side by '7'.
i = -1.142857143

Simplifying
i = -1.142857143
Solution
i = {-1.25, -1.142857143}

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