Class xi complex numbers worksheet (t)

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