Q.

If z1 and z2 are two complex numbers satisfying z12z2+2z2z1=i and if 0, z1, z2 form two non similar triangles and if αβ are the least angles in the two triangles then cot α+ cot β equals

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a

2

b

1

c

5

d

25

answer is B.

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Detailed Solution

z12z2=tt+1t=it2it+1=0t=i±142=(1+5)i2,(51)(i)2z1z2=(1+5)i or z1z2=(51)(i)
 

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cotα=1+5cotβ=51cotα+cotβ=25

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