Question Detail
Question
Given that z₁ = i and z₂ = 1-i, find z₁/z₂
Correct Answer
Option A is the correct answer.
Detailed Explanation
z₁/z₂ = i/(1-i). Multiply numerator and denominator by the conjugate (1+i): i(1+i)/((1-i)(1+i)) = i + i²/(1² - i²) = i - 1/(1+1) = (i-1)/2 = -1/2 + i/2. The magnitude is √[(1/2)² + (1/2)²] = √(1/4+1/4) = √(1/2) = 1/√2. The options given don't match this exactly. Option A is 1/2, which might be the real part or the magnitude squared?
Hint
Multiply numerator and denominator by the conjugate of the denominator.