(7+5i)(4-8i)=0

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Solution for (7+5i)(4-8i)=0 equation: 


Simplifying
(7 + 5i)(4 + -8i) = 0

Multiply (7 + 5i) * (4 + -8i)
(7(4 + -8i) + 5i * (4 + -8i)) = 0
((4 * 7 + -8i * 7) + 5i * (4 + -8i)) = 0
((28 + -56i) + 5i * (4 + -8i)) = 0
(28 + -56i + (4 * 5i + -8i * 5i)) = 0
(28 + -56i + (20i + -40i2)) = 0

Combine like terms: -56i + 20i = -36i
(28 + -36i + -40i2) = 0

Solving
28 + -36i + -40i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -9i + -10i2) = 0

Factor a trinomial.
4((1 + -2i)(7 + 5i)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5

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 = {0.5, -1.4}

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