(4-10i)(-2+5i)=

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Solution for (4-10i)(-2+5i)= equation: 


Simplifying
(4 + -10i)(-2 + 5i) = 0

Multiply (4 + -10i) * (-2 + 5i)
(4(-2 + 5i) + -10i * (-2 + 5i)) = 0
((-2 * 4 + 5i * 4) + -10i * (-2 + 5i)) = 0
((-8 + 20i) + -10i * (-2 + 5i)) = 0
(-8 + 20i + (-2 * -10i + 5i * -10i)) = 0
(-8 + 20i + (20i + -50i2)) = 0

Combine like terms: 20i + 20i = 40i
(-8 + 40i + -50i2) = 0

Solving
-8 + 40i + -50i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 20i + -25i2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 5i)' equal to zero and attempt to solve:

Simplifying
-2 + 5i = 0

Solving
-2 + 5i = 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 + 5i = 0 + 2

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

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

Divide each side by '5'.
i = 0.4

Simplifying
i = 0.4

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

Simplifying
2 + -5i = 0

Solving
2 + -5i = 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 + -5i = 0 + -2

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

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

Divide each side by '-5'.
i = 0.4

Simplifying
i = 0.4
Solution
i = {0.4, 0.4}

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