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Simplifying
(6i + -1I)(6i + I) = 0
Reorder the terms:
(-1I + 6i)(6i + I) = 0
Reorder the terms:
(-1I + 6i)(I + 6i) = 0
Multiply (-1I + 6i) * (I + 6i)
(-1I * (I + 6i) + 6i * (I + 6i)) = 0
((I * -1I + 6i * -1I) + 6i * (I + 6i)) = 0
((-1I2 + -6iI) + 6i * (I + 6i)) = 0
(-1I2 + -6iI + (I * 6i + 6i * 6i)) = 0
(-1I2 + -6iI + (6iI + 36i2)) = 0
Combine like terms: -6iI + 6iI = 0
(-1I2 + 0 + 36i2) = 0
(-1I2 + 36i2) = 0
Solving
-1I2 + 36i2 = 0
Solving for variable 'I'.
Move all terms containing I to the left, all other terms to the right.
Add '-36i2' to each side of the equation.
-1I2 + 36i2 + -36i2 = 0 + -36i2
Combine like terms: 36i2 + -36i2 = 0
-1I2 + 0 = 0 + -36i2
-1I2 = 0 + -36i2
Remove the zero:
-1I2 = -36i2
Divide each side by '-1'.
I2 = 36i2
Simplifying
I2 = 36i2
Take the square root of each side:
I = {-6i, 6i}
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