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

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


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

Multiply (4 + 3i) * (-2 + 5i)
(4(-2 + 5i) + 3i * (-2 + 5i)) = 0
((-2 * 4 + 5i * 4) + 3i * (-2 + 5i)) = 0
((-8 + 20i) + 3i * (-2 + 5i)) = 0
(-8 + 20i + (-2 * 3i + 5i * 3i)) = 0
(-8 + 20i + (-6i + 15i2)) = 0

Combine like terms: 20i + -6i = 14i
(-8 + 14i + 15i2) = 0

Solving
-8 + 14i + 15i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(-4 + -3i)' equal to zero and attempt to solve:

Simplifying
-4 + -3i = 0

Solving
-4 + -3i = 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 + -3i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3i = 0 + 4
-3i = 0 + 4

Combine like terms: 0 + 4 = 4
-3i = 4

Divide each side by '-3'.
i = -1.333333333

Simplifying
i = -1.333333333

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

Simplifying
2 + -5i = 0

Solving
2 + -5i = 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 + -5i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5i = 0 + -2
-5i = 0 + -2

Combine like terms: 0 + -2 = -2
-5i = -2

Divide each side by '-5'.
i = 0.4

Simplifying
i = 0.4
Solution
i = {-1.333333333, 0.4}

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