Express the complex quotient (3 + 4i) / (1 - 2i) in standard form a + b*i.
Answer and explanation
Correct answer: D. -1 + 2*i
- Step 1: Multiply numerator and denominator by the complex conjugate of the denominator, 1 + 2*i.
- Step 2: Numerator: (3 + 4i)(1 + 2i) = 3 + 6i + 4i + 8i^2 = 3 + 10i - 8 = -5 + 10*i.
- Step 3: Denominator: (1 - 2i)(1 + 2i) = 1^2 - (2*i)^2 = 1 - (-4) = 5.
- Step 4: Divide: (-5 + 10i) / 5 = -1 + 2i.
Answer
-1 + 2*i.
Why not the others: 1 + 2i has the wrong real sign from 3 - 8; -1 - 2i has the wrong imaginary sign; 3 - 2*i fails to expand the product.
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