(-1+7i)(6-7i)=

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Solution for (-1+7i)(6-7i)= equation:


Simplifying
(-1 + 7i)(6 + -7i) = 0

Multiply (-1 + 7i) * (6 + -7i)
(-1(6 + -7i) + 7i * (6 + -7i)) = 0
((6 * -1 + -7i * -1) + 7i * (6 + -7i)) = 0
((-6 + 7i) + 7i * (6 + -7i)) = 0
(-6 + 7i + (6 * 7i + -7i * 7i)) = 0
(-6 + 7i + (42i + -49i2)) = 0

Combine like terms: 7i + 42i = 49i
(-6 + 49i + -49i2) = 0

Solving
-6 + 49i + -49i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-6 + 7i)(1 + -7i) = 0

Subproblem 1

Set the factor '(-6 + 7i)' equal to zero and attempt to solve: Simplifying -6 + 7i = 0 Solving -6 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 7i = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7i = 0 + 6 7i = 0 + 6 Combine like terms: 0 + 6 = 6 7i = 6 Divide each side by '7'. i = 0.8571428571 Simplifying i = 0.8571428571

Subproblem 2

Set the factor '(1 + -7i)' equal to zero and attempt to solve: Simplifying 1 + -7i = 0 Solving 1 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -7i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7i = 0 + -1 -7i = 0 + -1 Combine like terms: 0 + -1 = -1 -7i = -1 Divide each side by '-7'. i = 0.1428571429 Simplifying i = 0.1428571429

Solution

i = {0.8571428571, 0.1428571429}

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