=(3+4i)(5-2i)

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Solution for =(3+4i)(5-2i) equation: 


Simplifying
0 = (3 + 4i)(5 + -2i)

Multiply (3 + 4i) * (5 + -2i)
0 = (3(5 + -2i) + 4i * (5 + -2i))
0 = ((5 * 3 + -2i * 3) + 4i * (5 + -2i))
0 = ((15 + -6i) + 4i * (5 + -2i))
0 = (15 + -6i + (5 * 4i + -2i * 4i))
0 = (15 + -6i + (20i + -8i2))

Combine like terms: -6i + 20i = 14i
0 = (15 + 14i + -8i2)

Solving
0 = 15 + 14i + -8i2

Solving for variable 'i'.

Combine like terms: 0 + -15 = -15
-15 + -14i + 8i2 = 15 + 14i + -8i2 + -15 + -14i + 8i2

Reorder the terms:
-15 + -14i + 8i2 = 15 + -15 + 14i + -14i + -8i2 + 8i2

Combine like terms: 15 + -15 = 0
-15 + -14i + 8i2 = 0 + 14i + -14i + -8i2 + 8i2
-15 + -14i + 8i2 = 14i + -14i + -8i2 + 8i2

Combine like terms: 14i + -14i = 0
-15 + -14i + 8i2 = 0 + -8i2 + 8i2
-15 + -14i + 8i2 = -8i2 + 8i2

Combine like terms: -8i2 + 8i2 = 0
-15 + -14i + 8i2 = 0

Factor a trinomial.
(-3 + -4i)(5 + -2i) = 0


Subproblem 1
Set the factor '(-3 + -4i)' equal to zero and attempt to solve:

Simplifying
-3 + -4i = 0

Solving
-3 + -4i = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4i = 0 + 3
-4i = 0 + 3

Combine like terms: 0 + 3 = 3
-4i = 3

Divide each side by '-4'.
i = -0.75

Simplifying
i = -0.75

Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve:

Simplifying
5 + -2i = 0

Solving
5 + -2i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2i = 0 + -5
-2i = 0 + -5

Combine like terms: 0 + -5 = -5
-2i = -5

Divide each side by '-2'.
i = 2.5

Simplifying
i = 2.5
Solution
i = {-0.75, 2.5}

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