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If $(a + b i)^{11} = x + i y,$ where $a, b, x, y \in R,$ then ${(b + a i)}^{11}$ equals

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y+ix

-y-ix

-x-iy

x+iy

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detailed solution

Correct option is B

(a+bi)11¯=x+iy¯⇒(a−bi)11=x−iy⇒[(−i)(b+ia)]11=−i(y+ix)⇒(−i)11(b+ia)11=−i(y+ix)As (−i)11=(−i)8(−1)3i3=i,We get (b+ia)11=−(y+ix)=−y−ix

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If (a+bi)11=x+iy, where a,b,x,y∈R, then (b+ai)11 equals

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Ready to Test Your Skills?

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If $(a + b i)^{11} = x + i y,$ where $a, b, x, y \in R,$ then ${(b + a i)}^{11}$ equals