CBSE Guess > Papers > Important Questions > Class XI > 2010 > Maths > Maths By Mr. Anil Kumar Tondak
CBSE CLASS XI
Complex Nos. & Quadratic Equations
Q.20. If Z is any non-zero complex number, prove that the multiplicative inverse of z is 
. Hence find the multiplicative inverse of 4
.
Q.21. Find the multiplicative inverse of the following complex numbers:
(i) 1 – i (ii) 
Q.22. Find multiplicative inverse of 2 + 
Q.23. Find the square root of – 15 – 8i.
Q.24. Find Modulus and Argument of :
(1) Z = -1 - 
(2) Z = 
Q.25. Find the value of x and y if
Q.26. If Z = 
Q.27. If 
, prove that x2 + y2 =1.
Q.28. If 
x2 + y2 = 1
Q.29. If (x + iy)3 = u + iv, then show that 
Q.30. If
, prove that 
Q.31. Put the following in the form r (cos q + sin q), where r is a positive real number and - p < q £ p : 
Q.32. Represent the complex number Z = 1 + i
in the Polar form.
Q.33. Express the following number in polar form: 
Q.34. Convert the complex number 
into polar form.
Q.35. Convert the complex number Z = 
in the Polar form.
Q.36. Convert the complex number 
in the polar form and represent them in Argand plane.
Q.37. If 
then find the least integral value of m.
Q.38. Let Z1 = 2 – i, Z2 = -2+ i, find Re
.
Q.39. If z1 and z2 are 1 – i and -2 + 4i find: Im 
Q.40 . If Z1= 4+ 7i, Z2=1- i, find Im(Z1.Z2)
Q.41. Solve: 2x2 – (3 + 7i)x – (3 – 9i) = 0
Q.42. Solve the equation:2z = 
.
Q.43 . Solve : 
.
Q.44. Solve for 
(i) 
(ii) -
Q.45. For any two complex numbers Z1 and Z2 Prove that:
Re (Z1Z2) =Re(Z1 )Re(Z2 )– Im(Z1)Im(Z2 )
Q.46. If z is the complex number then prove that:
(a) 
(b) 
Q.47. Find the number of non - zero integral solutions of the equation | 1 - t | x = 2x
Q.48. If Z is a complex number such that 
then prove that 
.
Q.49. Find the complex number, z satisfying the equations:
Q.50. Show that if 
Q.51. If a + ib = 
.
Q.52. If 
Q.53. Find the real value of such that 
is (i) purely real (ii) purely imaginary.
Q.54. If a and b are different complex numbers with | b| = 1, find
.
Paper By Mr. Anil Kumar Tondak
Email Id : anil_tondak@yahoo.com
Ph No.: 9811363962
