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

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


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

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

Combine like terms: -10i + 12i = 2i
(8 + 2i + -15i2) = 0

Solving
8 + 2i + -15i2 = 0

Solving for variable 'i'.

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

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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