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Simplifying
(5 + 3i)(5 + -3i) = 0
Multiply (5 + 3i) * (5 + -3i)
(5(5 + -3i) + 3i * (5 + -3i)) = 0
((5 * 5 + -3i * 5) + 3i * (5 + -3i)) = 0
((25 + -15i) + 3i * (5 + -3i)) = 0
(25 + -15i + (5 * 3i + -3i * 3i)) = 0
(25 + -15i + (15i + -9i2)) = 0
Combine like terms: -15i + 15i = 0
(25 + 0 + -9i2) = 0
(25 + -9i2) = 0
Solving
25 + -9i2 = 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 + -9i2 = 0 + -25
Combine like terms: 25 + -25 = 0
0 + -9i2 = 0 + -25
-9i2 = 0 + -25
Combine like terms: 0 + -25 = -25
-9i2 = -25
Divide each side by '-9'.
i2 = 2.777777778
Simplifying
i2 = 2.777777778
Take the square root of each side:
i = {-1.666666667, 1.666666667}
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