(2+3i)(2+3i)=0

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


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

Multiply (2 + 3i) * (2 + 3i)
(2(2 + 3i) + 3i * (2 + 3i)) = 0
((2 * 2 + 3i * 2) + 3i * (2 + 3i)) = 0
((4 + 6i) + 3i * (2 + 3i)) = 0
(4 + 6i + (2 * 3i + 3i * 3i)) = 0
(4 + 6i + (6i + 9i2)) = 0

Combine like terms: 6i + 6i = 12i
(4 + 12i + 9i2) = 0

Solving
4 + 12i + 9i2 = 0

Solving for variable 'i'.

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

Subproblem 1

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

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 = {-0.6666666667, -0.6666666667}

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