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Question: Answered & Verified by Expert
Let z1 and z2 be two complex numbers such that argz1-z2=π4 and z1,z2 satisfy the equation z-3=Re(z). Then the imaginary part z1+z2 is equal to
MathematicsComplex NumberJEE MainJEE Main 2021 (27 Aug Shift 2)
Solution:
1002 Upvotes Verified Answer
The correct answer is: 6
Let z1=x1+iy1,z2=x2+iy2
z1-z2=x1-x2+iy1-y2
argz1-z2=π4tan-1y1-y2x1-x2=π4
y1-y2=x1-x2----(1)
z1-3=Rez1x1-32+y12=x12
z2-3=Rez2x2-32+y22=x22
x1-32-x2-32+y12-y22=x12-x22
x1-x2x1+x2-6+y1-y2y1+y2=x1+x2x1-x2
x1+x2-6+y1+y2=x1+x2
y1+y2=6

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