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Question

If a+ibc+id=x+iy, then a2+b2c2+d2 is equal to

A
x2y2
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B
x2+y2
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C
(x+y)2
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D
(xy)2
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Solution

The correct option is B x2+y2
Given : a+ibc+id=x+iy
Now,
a2+b2c2+d2=(a+ib)(aib)(c+id)(cid)=a+ibc+id×aibcid=a+ibc+idׯ¯¯¯¯¯¯¯¯¯¯¯¯¯a+ib¯¯¯¯¯¯¯¯¯¯¯¯¯¯c+id=(x+iy)×(xiy)=x2+y2

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