JEE WEEKLY TEST MATHEMATICS (23.08.2025)

Deselect Answer

3. Express the given complex number i⁹+i¹⁹ in the form a+ib

1) 0   
2) 1+i
3) -1+i
4) 2+0i

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5. If (1+i)(x+iy)=2+4i then “5x” is

1) 11   
2) 13
3) 14   
4) 15

6. Find the conjugate of (1+i)³

1) -2+2i
2) -2-2i
3)  1-i   
4) 1-3i

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9. If the area of the triangle on the complex plane formed by the points z, iz and z+iz is square units, then |z| is

1) 5
2) 20
3) 15
4) none of these

10. Find the argument of z=1+i

1)  -π/4
2)  π
3) π/4
4)  π/6

11. If z₁=2+i, z₂=1+3i, then Re(z₁-z₂ )=

1) i
2)  1
3) 2i
4) 2

1) -i
2)1
3) i
4) -1

13. i²+i⁴+i⁶+… up to 2k+1 terms, for all k belongs to natural numbers N equals-

1) 1
2) -1
3) 0
4) none of these

14. If (x+iy)(3-4i)=(5+12i), then

1) 5/13
2) 13/5
3) 16
4) 65

15. If |z+4|≤3, then the maximum value of |z+1| is

1) 6
2) 0
3) 4 
4)10

1)  n=8 
2)  n=16
3) n=12
4) n=4

1) 2i 
2) 2
3) √2
4) 2√2

Deselect Answer

1. a=25, b=-8
2. a=25,b=8
3. a=5,b=4
4. none of theseDeselect Answer

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22. Which of the following is correct for any two complex numbers z₁ and z₂?

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23. The point represented by the complex number 2-i is rotated about origin through an angle π/2 in the clockwise direction, the new position of point is

1)  1+2i   
2) -1-2i
3)   2+i
4) -1+2i

24. If  for z=α+iβ, |z+2|=z+4(1+i , then α+β and αβ are the roots of the equation

1) 1
2) 12
3) 9
4) -9

Deselect Answer

1) line, y=-x   
2) imaginary axis
3) line, y=x
4) real axis

28. Let z be a complex number such that |z|+z=3+i. Then |z| is equal to

1) 3/5
2) 5/3
3) 5/4
4) 4/5

29. The equation |z-i|=|z-1|  represents

30. Let ω₁ be a point obtained by the rotation of z₁=5+4i about the origin through a right angle in the anticlockwise direction, and ω₂ be the point through a right angle in the clockwise direction. Then the principal argument ω₁-ω₂ is equal to