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

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


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

Multiply (8 + 5i) * (7 + 3i)
(8(7 + 3i) + 5i * (7 + 3i)) = 0
((7 * 8 + 3i * 8) + 5i * (7 + 3i)) = 0
((56 + 24i) + 5i * (7 + 3i)) = 0
(56 + 24i + (7 * 5i + 3i * 5i)) = 0
(56 + 24i + (35i + 15i2)) = 0

Combine like terms: 24i + 35i = 59i
(56 + 59i + 15i2) = 0

Solving
56 + 59i + 15i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(7 + 3i)' equal to zero and attempt to solve:

Simplifying
7 + 3i = 0

Solving
7 + 3i = 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 + 3i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3i = 0 + -7
3i = 0 + -7

Combine like terms: 0 + -7 = -7
3i = -7

Divide each side by '3'.
i = -2.333333333

Simplifying
i = -2.333333333

Subproblem 2
Set the factor '(8 + 5i)' equal to zero and attempt to solve:

Simplifying
8 + 5i = 0

Solving
8 + 5i = 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 + 5i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5i = 0 + -8
5i = 0 + -8

Combine like terms: 0 + -8 = -8
5i = -8

Divide each side by '5'.
i = -1.6

Simplifying
i = -1.6
Solution
i = {-2.333333333, -1.6}

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