Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let z 1 and z 2 be two complex numbers such that 
and 
satisfy the equation |z − 3| = Re(z). Then the imaginary part of z 1 + z 2 is equal to.
Text Solution
Verified by ExpertsThe correct answer is:
6
(6)
|z − 3| = Re(z)
let Z = x = iy
⇒ (x − 3) 2 + y 2 = x 2
⇒ x 2 + 9 − 6x + y 2 = x 2
⇒ y 2 = 6x – 9
and 
lie on the parabola mentioned in eq.(1)
Slope of PQ =1.
Let 
and 
Slope of 
Im(z 1 + z 2 ) = 3t 1 + 3t 2 = 3 (t 1 + t 2 ) = 3(2) = 6.00
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Let the lines and (here ) be normal to a circle . If the line is tangent to this circle , the…
Let a complex number ,satisfy Then, the largest value of is equal to
The least value of where is complex number which satisfies the inequality , is equal to:
The area of the triangle with vertices and is:
Let and be three sets defined as
Then the set
If the equation represents a circle where are real constants then which of the following conditio…