(7+8i)(7-i)=

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Solution for (7+8i)(7-i)= equation: 


Simplifying
(7 + 8i)(7 + -1i) = 0

Multiply (7 + 8i) * (7 + -1i)
(7(7 + -1i) + 8i * (7 + -1i)) = 0
((7 * 7 + -1i * 7) + 8i * (7 + -1i)) = 0
((49 + -7i) + 8i * (7 + -1i)) = 0
(49 + -7i + (7 * 8i + -1i * 8i)) = 0
(49 + -7i + (56i + -8i2)) = 0

Combine like terms: -7i + 56i = 49i
(49 + 49i + -8i2) = 0

Solving
49 + 49i + -8i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(7 + -1i)(7 + 8i) = 0


Subproblem 1
Set the factor '(7 + -1i)' equal to zero and attempt to solve:

Simplifying
7 + -1i = 0

Solving
7 + -1i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1i = 0 + -7
-1i = 0 + -7

Combine like terms: 0 + -7 = -7
-1i = -7

Divide each side by '-1'.
i = 7

Simplifying
i = 7

Subproblem 2
Set the factor '(7 + 8i)' equal to zero and attempt to solve:

Simplifying
7 + 8i = 0

Solving
7 + 8i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 8i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8i = 0 + -7
8i = 0 + -7

Combine like terms: 0 + -7 = -7
8i = -7

Divide each side by '8'.
i = -0.875

Simplifying
i = -0.875
Solution
i = {7, -0.875}

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