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

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


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

Multiply (2 + 3i) * (5 + -3i)
(2(5 + -3i) + 3i * (5 + -3i)) = 0
((5 * 2 + -3i * 2) + 3i * (5 + -3i)) = 0
((10 + -6i) + 3i * (5 + -3i)) = 0
(10 + -6i + (5 * 3i + -3i * 3i)) = 0
(10 + -6i + (15i + -9i2)) = 0

Combine like terms: -6i + 15i = 9i
(10 + 9i + -9i2) = 0

Solving
10 + 9i + -9i2 = 0

Solving for variable 'i'.

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

Subproblem 1

Set the factor '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667

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 = {1.666666667, -0.6666666667}

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