(2+3i)(8-5i)=0

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Solution for (2+3i)(8-5i)=0 equation:


Simplifying
(2 + 3i)(8 + -5i) = 0

Multiply (2 + 3i) * (8 + -5i)
(2(8 + -5i) + 3i * (8 + -5i)) = 0
((8 * 2 + -5i * 2) + 3i * (8 + -5i)) = 0
((16 + -10i) + 3i * (8 + -5i)) = 0
(16 + -10i + (8 * 3i + -5i * 3i)) = 0
(16 + -10i + (24i + -15i2)) = 0

Combine like terms: -10i + 24i = 14i
(16 + 14i + -15i2) = 0

Solving
16 + 14i + -15i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(8 + -5i)(2 + 3i) = 0

Subproblem 1

Set the factor '(8 + -5i)' equal to zero and attempt to solve: Simplifying 8 + -5i = 0 Solving 8 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5i = 0 + -8 -5i = 0 + -8 Combine like terms: 0 + -8 = -8 -5i = -8 Divide each side by '-5'. i = 1.6 Simplifying i = 1.6

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 = {1.6, -0.6666666667}

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