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

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


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

Multiply (8 + 4i) * (8 + i)
(8(8 + i) + 4i * (8 + i)) = 0
((8 * 8 + i * 8) + 4i * (8 + i)) = 0
((64 + 8i) + 4i * (8 + i)) = 0
(64 + 8i + (8 * 4i + i * 4i)) = 0
(64 + 8i + (32i + 4i2)) = 0

Combine like terms: 8i + 32i = 40i
(64 + 40i + 4i2) = 0

Solving
64 + 40i + 4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + 10i + i2) = 0

Factor a trinomial.
4((8 + i)(2 + i)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + i)' equal to zero and attempt to solve:

Simplifying
8 + i = 0

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

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

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

Simplifying
i = -8

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 = {-8, -2}

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