1-i-1-i50-x- iy -then find the value of x- y-A- 1-0B- 0-1 C- 0- i D- -1-0

The correct option is D ( 1,0)(1 i1+i)^50=x+iy (1 i1+i×1 i1 i)^50=x+iy ( 2i2)^50=x+iy ⇒( i)^50=( i)^4×12+2 ⇒ nbsp;( i)^4×12 ( i)^2 = 1+0i So, (x,y)=( 1,0) ...

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Byju's Answer

Standard XI

Mathematics

nCr Definitions and Properties

1-i/1+i50=x+ ...

Question

If ${(\frac{1 - i}{1 + i})}^{50} = x + i y$ ,then find the value of $(x, y)$ .

(0, 1)

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(1, 0)

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(0, i)

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(- 1, 0)

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Solution

The correct option is D $(- 1, 0)$
${(\frac{1 - i}{1 + i})}^{50} = x + i y {(\frac{1 - i}{1 + i} \times \frac{1 - i}{1 - i})}^{50} = x + i y {(\frac{- 2 i}{2})}^{50} = x + i y \Rightarrow (- i)^{50} = (- i)^{4 \times 12 + 2} \Rightarrow (- i)^{4 \times 12} (- i)^{2} = - 1 + 0 i So, (x, y) = (- 1, 0)$

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If (1−i1+i)50=x+iy ,then find the value of (x,y).

The correct option is D (−1,0)(1−i1+i)50=x+iy(1−i1+i×1−i1−i)50=x+iy(−2i2)50=x+iy⇒(−i)50=(−i)4×12+2⇒(−i)4×12(−i)2=−1+0iSo,(x,y)=(−1,0)

If ${(\frac{1 - i}{1 + i})}^{50} = x + i y$ ,then find the value of $(x, y)$ .