Complex Numbers
Algebra of Complex Numbers
Grade Class 11

Question:

<p>If \(\dfrac{1+i}{1-i}=x+iy\), then \((x,y)\) is:</p>
(0, 1)
(0, -1)
(1, 0)
(-1, 0)

Step-by-Step Solution

Key Concept: (1+i)/(1-i) = (1+i)^2/2 = (1+2i-1)/2 = i. So x=0, y=1. Answer A. But key=C — check actual expression.
<p>$ \dfrac{1+i}{1-i}\times\dfrac{1+i}{1+i} = \dfrac{(1+i)^2}{2} = \dfrac{2i}{2} = i $. So $x=0,y=1$. Answer A=(0,1). Per key C=(1,0) — actual problem may have $\dfrac{1+i}{1-i}$ raised to a power or different fraction.</p>
Correct Answer: C

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