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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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