If (x+iy)5=p+iq, then the value of 2(y+ix)5q+ip is
A
1
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B
2
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C
3
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D
4
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Solution
The correct option is B2 Given : (x+iy)5=p+iq Now, 2(y+ix)5q+ip=2i5(x−iy)5i(p−iq)=2(x−iy)5(p−iq)=2¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(x+iy)5¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(p+iq)=2¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(x+iy)5¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(p+iq)(∵(¯¯¯¯¯zn)=(¯¯¯z)n)=2¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯((x+iy)5p+iq)(∵¯¯¯¯¯z1¯¯¯¯¯z2=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(z1z2))=2×1=2