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

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


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

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

Combine like terms: -12i + -10i = -22i
(-8 + -22i + -15i2) = 0

Solving
-8 + -22i + -15i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 22i + 15i2) = 0

Factor a trinomial.
-1((4 + 5i)(2 + 3i)) = 0

Ignore the factor -1.

Subproblem 1
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

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 = {-0.8, -0.6666666667}

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