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Simplifying
(5 + 6i)(5 + -6i) = 0
Multiply (5 + 6i) * (5 + -6i)
(5(5 + -6i) + 6i * (5 + -6i)) = 0
((5 * 5 + -6i * 5) + 6i * (5 + -6i)) = 0
((25 + -30i) + 6i * (5 + -6i)) = 0
(25 + -30i + (5 * 6i + -6i * 6i)) = 0
(25 + -30i + (30i + -36i2)) = 0
Combine like terms: -30i + 30i = 0
(25 + 0 + -36i2) = 0
(25 + -36i2) = 0
Solving
25 + -36i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-25' to each side of the equation.
25 + -25 + -36i2 = 0 + -25
Combine like terms: 25 + -25 = 0
0 + -36i2 = 0 + -25
-36i2 = 0 + -25
Combine like terms: 0 + -25 = -25
-36i2 = -25
Divide each side by '-36'.
i2 = 0.6944444444
Simplifying
i2 = 0.6944444444
Take the square root of each side:
i = {-0.833333333, 0.833333333}
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