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Question

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 B 2
Given : (x+iy)5=p+iq
Now,
2(y+ix)5q+ip=2i5(xiy)5i(piq)=2(xiy)5(piq)=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

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