Simplify the complex number expression: (3 + 4i) / (1 - 2i) into standard a + bi form.
Answer and explanation
Correct answer: D. -1 + 2i
- Step 1: Multiply numerator and denominator by the complex conjugate of the denominator (1 + 2i):
- Step 2: Numerator: (3 + 4i)(1 + 2i) = 3 + 6i + 4i + 8i^2 = 3 + 10i - 8 = -5 + 10i.
- Step 3: Denominator: (1 - 2i)(1 + 2i) = 1^2 - (2i)^2 = 1 - 4(-1) = 1 + 4 = 5.
- Step 4: Divide: (-5 + 10i) / 5 = -1 + 2i.
Answer
-1 + 2i.
Why not the others: '1 + 2i' drops the negative sign on -5; '-1 - 2i' conjugates the result; '11/5 + 2i' multiplies 3*1 + 8 instead of 3 - 8 in the numerator.
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