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Question

If z4z]=2, Then the maximum value of |z| is equal tp

A
1+3
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B
1+5
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C
15
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D
51
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Solution

The correct option is C 1+5

Consider the following question.

Z=ρeiϕ


We know that.

|Z|=Z¯¯¯¯Z

(ρeiϕ4ρeiϕ)(ρeiϕ4ρeiϕ)=4

ρ28cos(2ϕ)+16ρ2=4

ρ42(2+4cos(2ϕ))ρ2+16=0


Now solving for ρ2

ρ2=2(1+2cos(2ϕ)±4cos(2ϕ)+2cos(4ϕ)1)

ρ2max=2(1+2+4+21)=2(3+5)

max|Z|=2(3+5)=1+5


Hence, this is the required answer.


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