(5-8i)(5-8i)=0

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


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

Multiply (5 + -8i) * (5 + -8i)
(5(5 + -8i) + -8i * (5 + -8i)) = 0
((5 * 5 + -8i * 5) + -8i * (5 + -8i)) = 0
((25 + -40i) + -8i * (5 + -8i)) = 0
(25 + -40i + (5 * -8i + -8i * -8i)) = 0
(25 + -40i + (-40i + 64i2)) = 0

Combine like terms: -40i + -40i = -80i
(25 + -80i + 64i2) = 0

Solving
25 + -80i + 64i2 = 0

Solving for variable 'i'.

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

Subproblem 1

Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625

Subproblem 2

Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625

Solution

i = {0.625, 0.625}

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