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Question

If z=a+ab lies in third quadrant, then ¯zz also lies in the third quadrant if



Your Answer
A

a > b > 0

Correct Answer
B

a < b < 0

Your Answer
C

b < a < 0

Your Answer
D

b > a > 0


Solution

The correct option is A

a < b < 0


Given that, z = x + ib lies in third quadrant

x < 0 and y < 0

Now ¯zz=xibx+ib=(xib)(xib)(x+ib)(xib)=x2y22ixbx2+b2=¯zz=x2b2x2+b22ixbx2+b2

Since, ¯zz also lies in third quadrant.

 x2b2x2+b2<0 and 2xbx2+b2<0 x2b2<0 and 2xb<0So, x<b<0

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