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

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


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

Multiply (5 + 4i) * (2 + 3i)
(5(2 + 3i) + 4i * (2 + 3i)) = 0
((2 * 5 + 3i * 5) + 4i * (2 + 3i)) = 0
((10 + 15i) + 4i * (2 + 3i)) = 0
(10 + 15i + (2 * 4i + 3i * 4i)) = 0
(10 + 15i + (8i + 12i2)) = 0

Combine like terms: 15i + 8i = 23i
(10 + 23i + 12i2) = 0

Solving
10 + 23i + 12i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(5 + 4i)' equal to zero and attempt to solve:

Simplifying
5 + 4i = 0

Solving
5 + 4i = 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 + 4i = 0 + -5

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

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

Divide each side by '4'.
i = -1.25

Simplifying
i = -1.25

Subproblem 2
Set the factor '(2 + 3i)' equal to zero and attempt to solve:

Simplifying
2 + 3i = 0

Solving
2 + 3i = 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 + 3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3i = 0 + -2
3i = 0 + -2

Combine like terms: 0 + -2 = -2
3i = -2

Divide each side by '3'.
i = -0.6666666667

Simplifying
i = -0.6666666667
Solution
i = {-1.25, -0.6666666667}

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