(7-4i)(5+8i)=

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Solution for (7-4i)(5+8i)= equation: 


Simplifying
(7 + -4i)(5 + 8i) = 0

Multiply (7 + -4i) * (5 + 8i)
(7(5 + 8i) + -4i * (5 + 8i)) = 0
((5 * 7 + 8i * 7) + -4i * (5 + 8i)) = 0
((35 + 56i) + -4i * (5 + 8i)) = 0
(35 + 56i + (5 * -4i + 8i * -4i)) = 0
(35 + 56i + (-20i + -32i2)) = 0

Combine like terms: 56i + -20i = 36i
(35 + 36i + -32i2) = 0

Solving
35 + 36i + -32i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(7 + -4i)(5 + 8i) = 0


Subproblem 1
Set the factor '(7 + -4i)' equal to zero and attempt to solve:

Simplifying
7 + -4i = 0

Solving
7 + -4i = 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 + -4i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4i = 0 + -7
-4i = 0 + -7

Combine like terms: 0 + -7 = -7
-4i = -7

Divide each side by '-4'.
i = 1.75

Simplifying
i = 1.75

Subproblem 2
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
Solution
i = {1.75, -0.625}

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