(4j+1)(4j-4)=

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Solution for (4j+1)(4j-4)= equation:


Simplifying
(4j + 1)(4j + -4) = 0

Reorder the terms:
(1 + 4j)(4j + -4) = 0

Reorder the terms:
(1 + 4j)(-4 + 4j) = 0

Multiply (1 + 4j) * (-4 + 4j)
(1(-4 + 4j) + 4j * (-4 + 4j)) = 0
((-4 * 1 + 4j * 1) + 4j * (-4 + 4j)) = 0
((-4 + 4j) + 4j * (-4 + 4j)) = 0
(-4 + 4j + (-4 * 4j + 4j * 4j)) = 0
(-4 + 4j + (-16j + 16j2)) = 0

Combine like terms: 4j + -16j = -12j
(-4 + -12j + 16j2) = 0

Solving
-4 + -12j + 16j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -3j + 4j2) = 0

Factor a trinomial.
4((-1 + -4j)(1 + -1j)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + -4j)' equal to zero and attempt to solve: Simplifying -1 + -4j = 0 Solving -1 + -4j = 0 Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4j = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4j = 0 + 1 -4j = 0 + 1 Combine like terms: 0 + 1 = 1 -4j = 1 Divide each side by '-4'. j = -0.25 Simplifying j = -0.25

Subproblem 2

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

Solution

j = {-0.25, 1}

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