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

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


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

Multiply (-2 + 4i) * (7 + 2i)
(-2(7 + 2i) + 4i * (7 + 2i)) = 0
((7 * -2 + 2i * -2) + 4i * (7 + 2i)) = 0
((-14 + -4i) + 4i * (7 + 2i)) = 0
(-14 + -4i + (7 * 4i + 2i * 4i)) = 0
(-14 + -4i + (28i + 8i2)) = 0

Combine like terms: -4i + 28i = 24i
(-14 + 24i + 8i2) = 0

Solving
-14 + 24i + 8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 12i + 4i2) = 0

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

Ignore the factor 2.

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 '(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 = {-3.5, 0.5}

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