UPSEE Solved Model Paper 1

Let, 𝑧 = 𝑥 + 𝑖𝑦, then

−

𝑧

= 𝑥 − 𝑖𝑦
⇒ 𝑧 +

−

𝑧

= 2𝑥
=

2+ − z

2

= x
and |z - 2| = √(x−2)2+y2
NOW 𝑧 +

−

𝑧

= 2|𝑧 − 2|
⇒ x = √(x−2)2+y2
⇒ x2 = (x−2)2+y2
⇒ x2 = x2+4−4x+y2
x =

y2+4

4

Now let two complex no. satisfied the condition are
z1 = (x1+iy1) and z2 = (x2+iy2)
then, z1 = (

y12+4

4

+iy1) and z2 = (

y22+4

4

+iy2)
z2−z2 = (

y12−y22

4

+i(y1−y2))
arg (z1−z2) = tan−1(

y1−y2

(y12−y22) 4

)
=

1

√3

=

4

y1+y2

= 4√3
z1+z2 = (

y12+y22+8

4

+i(y1+y2))
Img (𝑧1+𝑧2) = 𝑦1+𝑦2
= 4√3