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Question

If z=x+iy lies in the third quadrant, then ¯¯¯zz also lies in the third quadrant if

A
x>y>0
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B
x<y<0
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C
y<x<0
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D
y>x>0
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Solution

The correct option is C y<x<0
Solution -

z=x+iy lines in third quadrant

¯zz=xiyx+iy=xiyx+iy×xiyxiy=(xiy)2x2+y2=x2y22ixyx2+y2

¯zz=x2y2x2+y22ixyx2+y2

For it to be in third quadrant

y<x<0


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