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

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


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

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

Combine like terms: -56i + 12i = -44i
(28 + -44i + -24i2) = 0

Solving
28 + -44i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -11i + -6i2) = 0

Factor a trinomial.
4((1 + -2i)(7 + 3i)) = 0

Ignore the factor 4.

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

Simplifying
1 + -2i = 0

Solving
1 + -2i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5

Subproblem 2
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
Solution
i = {0.5, -2.333333333}

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