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

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


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

Multiply (4 + 5i) * (7 + -8i)
(4(7 + -8i) + 5i * (7 + -8i)) = 0
((7 * 4 + -8i * 4) + 5i * (7 + -8i)) = 0
((28 + -32i) + 5i * (7 + -8i)) = 0
(28 + -32i + (7 * 5i + -8i * 5i)) = 0
(28 + -32i + (35i + -40i2)) = 0

Combine like terms: -32i + 35i = 3i
(28 + 3i + -40i2) = 0

Solving
28 + 3i + -40i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(7 + -8i)' equal to zero and attempt to solve:

Simplifying
7 + -8i = 0

Solving
7 + -8i = 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 + -8i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8i = 0 + -7
-8i = 0 + -7

Combine like terms: 0 + -7 = -7
-8i = -7

Divide each side by '-8'.
i = 0.875

Simplifying
i = 0.875

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 = {0.875, -0.8}

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