The document is a worksheet containing 21 practice problems related to complex numbers for Class XI students. It provides the questions, answers, and additional context including the name and address of the science classes providing the worksheet. The worksheet covers topics such as operations and properties involving complex numbers, roots of complex equations, and representations of complex numbers in the complex plane.

1. CLASS XI COMPLEX NUMBERS WORKSHEET (T) – PART 2
STHITPRAGYA SCIENCE CLASSES, GANDHIDHAM
ADVANCED MATHEMATICS FOR JEE | BITSAT| GUJCET| OLYMPIADS | IX, X, XI, XII, XII +
MISHAL CHAUHAN (M.Tech, IIT Delhi)
Address 1: Near Gayatri Mandir, Opp. PGVCL Office, Shaktinagar Address 2: Sec-5, G.H.B, Gandhidham
Contact: 9879639888 Email:sthitpragyaclasses@gmail.com
Q. 1 If  isnonreal and  = 5
1 thenthe value of
2 2 1
|1 |
2
 
  
isequal to
(a) 4 (b) 2 (c) 1 (d) none of these
Q. 2 The value of amp (i) + amp (i2
),where i 1
  and 3
1
  = nonreal,is
(a) 0 (b)
2

(c)  (d) none of these
Q. 3 If , be two complex numbersthen|2
|+||2
isequal to
(a) 2 2
1
(| | | | )
2
       (b) 2 2
1
(| | | | )
2
      
(c) 2 2
| | | |
      (d) none of these
Q. 4 The setof valuesof a  R for whichx2
+ i(a – 1)x + 5 = 0 will have apairconjugate complex roots
is
(a) R (b) {1} (c) {a|a2
– 2a + 21 > 0} (d) none of these
Q. 5 Nonreal complexnumberszsatisfyingthe equationz3
+ 2z2
+ 3z + 2 = 0 are
(a)
1 7
2
  
(b)
1 7i 1 7i
,
2 2
 
(c)
1 7i 1 7i
i, ,
2 2
   
 (d) none of these
Q. 6 For a complex numberz,the minimumvalueof |z|+ |z -2 | is
(a) 1 (b) 2 (c) 3 (d) none of these
Q. 7 If |z| = 1 then
1 z
1 z


is equal to
(a) z (b) z (c) z z
 (d) none of these
Q. 8 If  isa nonreal cube root of unitythen|n
|,n  Z , is equal to
(a) 1 (b) 3 (c) 0 (d) none of these
Q. 9 If z be a complex numbersatisfyingz4
+ z3
+ 2z2
+ z + 1 = 0 then|z| is
(a)
1
2
(b)
3
4
(c) 1 (d) none of these
Q. 10 Let z1 = a + ib,z2= p + iqbe twounimodularcomplexnumberssuchthatIm( 1 2
z z ) = 1. If 1 = a +
ip, 2 = b + iq then
(a) Re(12) = 1 (b) Im(12) = 1 (c) Re(12) = 0 (d) Im( 1 2
  ) = 1
Q. 10 If |z1 – 1| < 1, |z2 – 2| < 2, |z3 – 3| < 3 then|z1 + z2 + z3|

2. CLASS XI COMPLEX NUMBERS WORKSHEET (T) – PART 2
STHITPRAGYA SCIENCE CLASSES, GANDHIDHAM
ADVANCED MATHEMATICS FOR JEE | BITSAT| GUJCET| OLYMPIADS | IX, X, XI, XII, XII +
MISHAL CHAUHAN (M.Tech, IIT Delhi)
Address 1: Near Gayatri Mandir, Opp. PGVCL Office, Shaktinagar Address 2: Sec-5, G.H.B, Gandhidham
Contact: 9879639888 Email:sthitpragyaclasses@gmail.com
(a) is lessthan6 (b) ismore than3 (c) is lessthan12 (d) liesbetween6and 12
Q. 11 If
2
1/2 2
| z | 2 | z | 4
log
2 | z | 1
 

< 0 thenthe regiontracedby z is
(a) |z| < 3 (b) 1 < |z| < 3 (c) |z| > 1 (d) |z| < 2
Q. 12
z 1
1
z 1



represents
(a) a circle (b) an ellipse (c) a straightline (d) none of these
Q. 13 If 2z1 – 3z2 + z3 = 0 thenz1,z2, z3 are representedby
(a) three verticesof a triangle (b) three collinearpoints
(c) three verticesof a rhombus (d) none of these
Q. 14 If A,B, C are three pointsinthe Argandplane representingthe complex numbersz1,z2,z3 such
that 2 3
1
z z
z
1
 

 
, where  R, thenthe distance of A fromthe line BCis
(a)  (b)
1

 
(c) 1 (d) 0
Q. 15 The rootsof the equation1+ z + z3
+ z4
= 0 are representedbythe verticesof
(a) a square (b) an equilateral triangle (c) a rhombus (d) none of these
Q. 16 If
z 4 1
Re
2z i 2

 

 

 
thenz isrepresentedbyapointlyingon
(a) a circle (b) an ellipse (c) a straightline (d) none of these
Q. 17 The angle thatthe vector representingthe complex number 25
1
( 3 i)

makeswiththe positive
directionof the real axisis
(a)
2
3

(b)
6

 (c)
5
6

(d)
6

Q. 18 If |z1 + z2| = |z1 – z2| then
(a) |amp z1 – amp z2| =
2

(b) |amp z1 – amp z2| = 
(c) 1
2
z
z
is purely real (d) 1
2
z
z
is purely imaginary
Q. 19 If |z1 + z2|2
= |z1|2
+ |z2|2
then

3. CLASS XI COMPLEX NUMBERS WORKSHEET (T) – PART 2
STHITPRAGYA SCIENCE CLASSES, GANDHIDHAM
ADVANCED MATHEMATICS FOR JEE | BITSAT| GUJCET| OLYMPIADS | IX, X, XI, XII, XII +
MISHAL CHAUHAN (M.Tech, IIT Delhi)
Address 1: Near Gayatri Mandir, Opp. PGVCL Office, Shaktinagar Address 2: Sec-5, G.H.B, Gandhidham
Contact: 9879639888 Email:sthitpragyaclasses@gmail.com
(a) 1
2
z
z
is purely real (b) 1
2
z
z
is purely imaginary (c) 1 2 2 1
z z z z 0
  (d)
1
2
z
amp
z 2


Q. 20 Let
2 2
1 2
( 3 i) .(1 3i) (1 3i) .( 3 i)
z ,z
1 i 1 i
   
 
 
. Then
(a) |z1| = |z2| (b) amp z1 + amp z2 = 0 (c) 3|z1| = |z2| (d) 3amp z1 + amp
z2 = 0
Q. 21 The value of 4n-1
+ 4n-2
+ 4n-3
, n  N and  is a nonreal fourth root of unity, is
(a) 0 (b) -1 (c) 3 (d) none of these