JEE Main20254 Apr 2025Morning ShiftMathematicsComplex NumberActual

Let A= z C:|z-2-i|=3 , B= z C: Re (z-i z)=2 and S=A B . Then _ z S |z|^2 is equal to ________ .

Correct answer

Step-by-step solution

Let z=x+i y aligned & A:|z-2-i|=3 & |(x-2)+(y-1) i|=3 & (x-2)^2+(y-1)^2=9 ....(1) & B= Re (z-i z)=2 & Re ((x+y)+i(y-x))=2 & x+y=2....(2) aligned . On solving (1) and (2) we get aligned & x= 3 17 2 , y= 1 17 2 & _ z ~s |z|^2= 1 4 [2 26+2 18] & 88 4 =22 aligned

Practice Complex Number on Quantrex Academy →

More from Complex Number

The number of values of z C , satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5 , is: 2026 Let S = z C : z^2 + 6 ,iz - 3 = 0 . Then _ z S z^8 is equal to : 2026 Let the set of all values of k R such that the equation z( z + 2 + i) + k(2 + 3i) = 0 , z C , has at least one solution, be the interval [ , ] . Then 9( + ) is equal to: 2026 Let z₁, z₂ C be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 . Then |z₁|^2 + |z₂|^2 is equal to : 2026 Let S= z C : z^2+4z+16=0 . Then _ z S |z+ 3 i|^2 is equal to: 2026 Let z be a complex number such that |z+2| = |z-2| and ( z+3 z-i ) = 4 . Then |z|^2 is equal to: 2026 Let the circles C₁ : |z| = r and C₂ : |z - 3 - 4i| = 5 , z C , be such that C₂ lies within C₁ . If z₁ moves on C₁ , z₂ moves on C₂ and |z₁ - z₂| = 2 , then |z₁ - z₂| is equal to: 2026 Let x and y be real numbers such that 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i , i = -1 . Then the value of 10(x - 3y) is : 2026 Full Complex Number list All JEE Main PYQs