(2+3i)(1-i)=5+i

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Solution for (2+3i)(1-i)=5+i equation:


Simplifying
(2 + 3i)(1 + -1i) = 5 + i

Multiply (2 + 3i) * (1 + -1i)
(2(1 + -1i) + 3i * (1 + -1i)) = 5 + i
((1 * 2 + -1i * 2) + 3i * (1 + -1i)) = 5 + i
((2 + -2i) + 3i * (1 + -1i)) = 5 + i
(2 + -2i + (1 * 3i + -1i * 3i)) = 5 + i
(2 + -2i + (3i + -3i2)) = 5 + i

Combine like terms: -2i + 3i = 1i
(2 + 1i + -3i2) = 5 + i

Solving
2 + 1i + -3i2 = 5 + i

Solving for variable 'i'.

Reorder the terms:
2 + -5 + 1i + -1i + -3i2 = 5 + i + -5 + -1i

Combine like terms: 2 + -5 = -3
-3 + 1i + -1i + -3i2 = 5 + i + -5 + -1i

Combine like terms: 1i + -1i = 0
-3 + 0 + -3i2 = 5 + i + -5 + -1i
-3 + -3i2 = 5 + i + -5 + -1i

Reorder the terms:
-3 + -3i2 = 5 + -5 + i + -1i

Combine like terms: 5 + -5 = 0
-3 + -3i2 = 0 + i + -1i
-3 + -3i2 = i + -1i

Combine like terms: i + -1i = 0
-3 + -3i2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1 + i2) = 0

Ignore the factor -3.

Subproblem 1

Set the factor '(1 + i2)' equal to zero and attempt to solve: Simplifying 1 + i2 = 0 Solving 1 + i2 = 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 + i2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i2 = 0 + -1 i2 = 0 + -1 Combine like terms: 0 + -1 = -1 i2 = -1 Simplifying i2 = -1 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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