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Simplifying abs(z + -3i) = abs(4 + 2i) Reorder the terms: abs(-3i + z) = abs(4 + 2i) (-3i * abs + z * abs) = abs(4 + 2i) (-3abis + absz) = abs(4 + 2i) -3abis + absz = (4 * abs + 2i * abs) Reorder the terms: -3abis + absz = (2abis + 4abs) -3abis + absz = (2abis + 4abs) Solving -3abis + absz = 2abis + 4abs Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2abis' to each side of the equation. -3abis + -2abis + absz = 2abis + -2abis + 4abs Combine like terms: -3abis + -2abis = -5abis -5abis + absz = 2abis + -2abis + 4abs Combine like terms: 2abis + -2abis = 0 -5abis + absz = 0 + 4abs -5abis + absz = 4abs Add '-4abs' to each side of the equation. -5abis + -4abs + absz = 4abs + -4abs Combine like terms: 4abs + -4abs = 0 -5abis + -4abs + absz = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-5i + -4 + z) = 0Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve: Simplifying abs = 0 Solving abs = 0 Move all terms containing a to the left, all other terms to the right. Simplifying abs = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5i + -4 + z)' equal to zero and attempt to solve: Simplifying -5i + -4 + z = 0 Reorder the terms: -4 + -5i + z = 0 Solving -4 + -5i + z = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + -5i + 4 + z = 0 + 4 Reorder the terms: -4 + 4 + -5i + z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5i + z = 0 + 4 -5i + z = 0 + 4 Combine like terms: 0 + 4 = 4 -5i + z = 4 Add '5i' to each side of the equation. -5i + 5i + z = 4 + 5i Combine like terms: -5i + 5i = 0 0 + z = 4 + 5i z = 4 + 5i Add '-1z' to each side of the equation. z + -1z = 4 + 5i + -1z Combine like terms: z + -1z = 0 0 = 4 + 5i + -1z Simplifying 0 = 4 + 5i + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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