(2+4i)(7-3i)=

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Solution for (2+4i)(7-3i)= equation: 


Simplifying
(2 + 4i)(7 + -3i) = 0

Multiply (2 + 4i) * (7 + -3i)
(2(7 + -3i) + 4i * (7 + -3i)) = 0
((7 * 2 + -3i * 2) + 4i * (7 + -3i)) = 0
((14 + -6i) + 4i * (7 + -3i)) = 0
(14 + -6i + (7 * 4i + -3i * 4i)) = 0
(14 + -6i + (28i + -12i2)) = 0

Combine like terms: -6i + 28i = 22i
(14 + 22i + -12i2) = 0

Solving
14 + 22i + -12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 11i + -6i2) = 0

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

Ignore the factor 2.

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 '(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
Solution
i = {2.333333333, -0.5}

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