(8+3i)(7-2i)=

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Solution for (8+3i)(7-2i)= equation: 


Simplifying
(8 + 3i)(7 + -2i) = 0

Multiply (8 + 3i) * (7 + -2i)
(8(7 + -2i) + 3i * (7 + -2i)) = 0
((7 * 8 + -2i * 8) + 3i * (7 + -2i)) = 0
((56 + -16i) + 3i * (7 + -2i)) = 0
(56 + -16i + (7 * 3i + -2i * 3i)) = 0
(56 + -16i + (21i + -6i2)) = 0

Combine like terms: -16i + 21i = 5i
(56 + 5i + -6i2) = 0

Solving
56 + 5i + -6i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(7 + -2i)' equal to zero and attempt to solve:

Simplifying
7 + -2i = 0

Solving
7 + -2i = 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 + -2i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2i = 0 + -7
-2i = 0 + -7

Combine like terms: 0 + -7 = -7
-2i = -7

Divide each side by '-2'.
i = 3.5

Simplifying
i = 3.5

Subproblem 2
Set the factor '(8 + 3i)' equal to zero and attempt to solve:

Simplifying
8 + 3i = 0

Solving
8 + 3i = 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 + 3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3i = 0 + -8
3i = 0 + -8

Combine like terms: 0 + -8 = -8
3i = -8

Divide each side by '3'.
i = -2.666666667

Simplifying
i = -2.666666667
Solution
i = {3.5, -2.666666667}

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