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Question

Match List I with List II and select the correct answer using the code given below the lists :

List IList II (A)Let z,ω,α be complex numbers such that(P)0|z|=|ω|=4 and α=z¯¯¯ω16+z ¯¯¯ω. Then Re (α) is equal to (B)If x=p+iq is a complex number such that(Q)3x2=3+4i and x3=2+11i, where i=1,then p+q is equal to(C)Number of complex number(s) z satisfying the(R)4equation ¯¯¯z=iz2, where i=1, is equal to(D)If zC satisfies |z+2i|=5, then the(S)5maximum value of |3z+97i|4 is equal to

Which of the following is the only CORRECT combination?

A
(C)(S), (D)(P)
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B
(C)(P), (D)(Q)
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C
(C)(Q), (D)(R)
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D
(C)(R), (D)(S)
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Solution

The correct option is D (C)(R), (D)(S)
(C)
We have ¯¯¯z=iz2
Put z=x+iy
xiy=i(x2y2+2ixy)
On solving, we get
z=0+i0,i,32i2,32i2
Hence, there are four solutions.

(D)
|3z+97i|=|(3z+63i)+(34i)||3z+63i|+|34i|=3|z+2i|+5=20

max(|3z+97i|4)=204=5

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