(2+4i)(8-i)=

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Solution for (2+4i)(8-i)= equation:


Simplifying
(2 + 4i)(8 + -1i) = 0

Multiply (2 + 4i) * (8 + -1i)
(2(8 + -1i) + 4i * (8 + -1i)) = 0
((8 * 2 + -1i * 2) + 4i * (8 + -1i)) = 0
((16 + -2i) + 4i * (8 + -1i)) = 0
(16 + -2i + (8 * 4i + -1i * 4i)) = 0
(16 + -2i + (32i + -4i2)) = 0

Combine like terms: -2i + 32i = 30i
(16 + 30i + -4i2) = 0

Solving
16 + 30i + -4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 15i + -2i2) = 0

Factor a trinomial.
2((8 + -1i)(1 + 2i)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(8 + -1i)' equal to zero and attempt to solve: Simplifying 8 + -1i = 0 Solving 8 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1i = 0 + -8 -1i = 0 + -8 Combine like terms: 0 + -8 = -8 -1i = -8 Divide each side by '-1'. i = 8 Simplifying i = 8

Subproblem 2

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

Solution

i = {8, -0.5}

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