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Simplifying
(-3i + 4)(3i + 4) = 0
Reorder the terms:
(4 + -3i)(3i + 4) = 0
Reorder the terms:
(4 + -3i)(4 + 3i) = 0
Multiply (4 + -3i) * (4 + 3i)
(4(4 + 3i) + -3i * (4 + 3i)) = 0
((4 * 4 + 3i * 4) + -3i * (4 + 3i)) = 0
((16 + 12i) + -3i * (4 + 3i)) = 0
(16 + 12i + (4 * -3i + 3i * -3i)) = 0
(16 + 12i + (-12i + -9i2)) = 0
Combine like terms: 12i + -12i = 0
(16 + 0 + -9i2) = 0
(16 + -9i2) = 0
Solving
16 + -9i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-16' to each side of the equation.
16 + -16 + -9i2 = 0 + -16
Combine like terms: 16 + -16 = 0
0 + -9i2 = 0 + -16
-9i2 = 0 + -16
Combine like terms: 0 + -16 = -16
-9i2 = -16
Divide each side by '-9'.
i2 = 1.777777778
Simplifying
i2 = 1.777777778
Take the square root of each side:
i = {-1.333333333, 1.333333333}
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