(7+3i)(8+4i)=0

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Solution for (7+3i)(8+4i)=0 equation: 


Simplifying
(7 + 3i)(8 + 4i) = 0

Multiply (7 + 3i) * (8 + 4i)
(7(8 + 4i) + 3i * (8 + 4i)) = 0
((8 * 7 + 4i * 7) + 3i * (8 + 4i)) = 0
((56 + 28i) + 3i * (8 + 4i)) = 0
(56 + 28i + (8 * 3i + 4i * 3i)) = 0
(56 + 28i + (24i + 12i2)) = 0

Combine like terms: 28i + 24i = 52i
(56 + 52i + 12i2) = 0

Solving
56 + 52i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + 13i + 3i2) = 0

Factor a trinomial.
4((7 + 3i)(2 + i)) = 0

Ignore the factor 4.

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 '(2 + i)' equal to zero and attempt to solve:

Simplifying
2 + i = 0

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

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

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

Simplifying
i = -2
Solution
i = {-2.333333333, -2}

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