Q.

If Ζ  is a complex number lying in first quadrant such that Re(Ζ)+Im(Ζ)=3  then the maximum value of  (Re(Ζ))2.Im(Ζ)   is

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a

2

b

3

c

4

d

6

answer is C.

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Detailed Solution

x+y=3⇒2.x2+y=3 A.M≥G.M⇒2.x2+y3≥[(x2)2y]1/3 ⇒    1≥(x2y4)1/3 ⇒    x2y≤4
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