(8+7i)(5-3i)=

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Solution for (8+7i)(5-3i)= equation: 


Simplifying
(8 + 7i)(5 + -3i) = 0

Multiply (8 + 7i) * (5 + -3i)
(8(5 + -3i) + 7i * (5 + -3i)) = 0
((5 * 8 + -3i * 8) + 7i * (5 + -3i)) = 0
((40 + -24i) + 7i * (5 + -3i)) = 0
(40 + -24i + (5 * 7i + -3i * 7i)) = 0
(40 + -24i + (35i + -21i2)) = 0

Combine like terms: -24i + 35i = 11i
(40 + 11i + -21i2) = 0

Solving
40 + 11i + -21i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + -3i)(8 + 7i) = 0


Subproblem 1
Set the factor '(5 + -3i)' equal to zero and attempt to solve:

Simplifying
5 + -3i = 0

Solving
5 + -3i = 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 + -3i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3i = 0 + -5
-3i = 0 + -5

Combine like terms: 0 + -5 = -5
-3i = -5

Divide each side by '-3'.
i = 1.666666667

Simplifying
i = 1.666666667

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 = {1.666666667, -1.142857143}

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