(7+5i)*(7-8i)=

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Solution for (7+5i)*(7-8i)= equation: 


Simplifying
(7 + 5i)(7 + -8i) = 0

Multiply (7 + 5i) * (7 + -8i)
(7(7 + -8i) + 5i * (7 + -8i)) = 0
((7 * 7 + -8i * 7) + 5i * (7 + -8i)) = 0
((49 + -56i) + 5i * (7 + -8i)) = 0
(49 + -56i + (7 * 5i + -8i * 5i)) = 0
(49 + -56i + (35i + -40i2)) = 0

Combine like terms: -56i + 35i = -21i
(49 + -21i + -40i2) = 0

Solving
49 + -21i + -40i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(7 + -8i)(7 + 5i) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + 5i)' equal to zero and attempt to solve:

Simplifying
7 + 5i = 0

Solving
7 + 5i = 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 + 5i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5i = 0 + -7
5i = 0 + -7

Combine like terms: 0 + -7 = -7
5i = -7

Divide each side by '5'.
i = -1.4

Simplifying
i = -1.4
Solution
i = {0.875, -1.4}

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