(8+10i)*(5-8i)=

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Solution for (8+10i)*(5-8i)= equation: 


Simplifying
(8 + 10i)(5 + -8i) = 0

Multiply (8 + 10i) * (5 + -8i)
(8(5 + -8i) + 10i * (5 + -8i)) = 0
((5 * 8 + -8i * 8) + 10i * (5 + -8i)) = 0
((40 + -64i) + 10i * (5 + -8i)) = 0
(40 + -64i + (5 * 10i + -8i * 10i)) = 0
(40 + -64i + (50i + -80i2)) = 0

Combine like terms: -64i + 50i = -14i
(40 + -14i + -80i2) = 0

Solving
40 + -14i + -80i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -7i + -40i2) = 0

Factor a trinomial.
2((5 + -8i)(4 + 5i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -8i)' equal to zero and attempt to solve:

Simplifying
5 + -8i = 0

Solving
5 + -8i = 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 + -8i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8i = 0 + -5
-8i = 0 + -5

Combine like terms: 0 + -5 = -5
-8i = -5

Divide each side by '-8'.
i = 0.625

Simplifying
i = 0.625

Subproblem 2
Set the factor '(4 + 5i)' equal to zero and attempt to solve:

Simplifying
4 + 5i = 0

Solving
4 + 5i = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5i = 0 + -4
5i = 0 + -4

Combine like terms: 0 + -4 = -4
5i = -4

Divide each side by '5'.
i = -0.8

Simplifying
i = -0.8
Solution
i = {0.625, -0.8}

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