Important Questions for CBSE Class 11 Maths Chapter 5 - Complex Numbers and Quadratic Equations
CBSE Class 11 Maths Chapter-5 Important Questions - Free PDF Download
1 Marks Questions
1. Evaluate i-39
Ans. 
2. Solved the quadratic equation 
Ans. 
3. If 
= 1, then find the least positive integral value of m.
Ans. 
4. Evaluate (1+ i)4
Ans. 
5. Find the modulus of 
Ans. Let z =
6. Express in the form of a + ib. (1+3i)-1
Ans. 
7. Explain the fallacy in -1 = i. i. = 
Ans. 
is okay but
is wrong.
8. Find the conjugate of 
Ans. Let z =
9. Find the conjugate of – 3i – 5.
Ans. Let z = 3i – 5
10. Let z1 = 2 – i, z2 = -2+i Find Re 
Ans. z1 z2 = (2 – i)(-2 + i)
11. Express in the form of a + ib (3i-7) + (7-4i) – (6+3i) + i23
Ans. Let
Z = 
12. Find the conjugate of 
Ans. 
13. Solve for x and y, 3x + (2x-y) i= 6 – 3i
Ans. 3x = 6
x = 2
2x – y = - 3
2 × 2 – y = - 3
- y = - 3 – 4
y = 7
14. Find the value of 1+i2 + i4 + i6 + i8 + ---- + i20
Ans.
15. Multiply 3-2i by its conjugate.
Ans.Let z = 3 – 2i
16. Find the multiplicative inverse 4 – 3i.
Ans. Let z = 4 – 3i
17. Express in term of a + ib
Ans. 
18. Evaluate 
Ans.
19. If 1, w, w2 are three cube root of unity, show that (1 – w + w2) (1 + w – w2) = 4
Ans.(1 – w + w2) (1 + w – w2)
(1 + w2 - w) (1 + w – w2)
20. Find that sum product of the complex number 
Ans. 
21. Write the real and imaginary part 1 – 2i2
Ans. Let z = 1 – 2i2
=1 – 2 (-1)
= 1 + 2
= 3
= 3 + 0.i
Re (z) = 3, Im (z) = 0
22. If two complex number z1, z2 are such that |z1| = |z2|, is it then necessary that z1 = z2
Ans.Let z1 = a + ib
23. Find the conjugate and modulus of 
Ans. Let 
24. Find the number of non zero integral solution of the equation |1-i|x = 2x
Ans. 
Which is false no value of x satisfies.
25. If (a + ib) (c + id) (e + if) (g + ih) = A + iB then show that
Ans. 
4 Marks Questions
1.If x + ί y = 
Prove that x2 + y2 = 1
Ans.
taking conjugate both side
x2 + y2 = 1
[i2 = -1
2.Find real θ such that 
is purely real.
Ans.
For purely real
Im (z) = 0
3.Find the modulus of 
Ans.
4.If 
then Show that 
Ans.
5.If x – iy = 
Prove that 
Ans.
Taking conjugate both side
6.If 
, where a, b, c are real prove that a2+b2 = 1 and 
Ans.
a2 + b2 = 1
7.If z1 = 2-i and Z2 = 1+i Find 
Ans.z1 + z2 + 1 = 2 – i + 1+ i + 1 = 4
8.If (p + iq)2 = x + iy Prove that (p2 + q2)2 = x2 + y2
Ans.(p + iq)2 = x + iy (i)
Taking conjugate both side
(p – iq)2 = x –iy (ii)
(i) × (ii)
9.If 
Ans.
Taking conjugate both side
10.If 
Ans.
11.Solve 
Ans.
12.Find the modulus 
Ans.i25 + (1+3i)3
13.If 
Ans. (i) (Given)
(ii) [taking conjugate both side
(i) × (ii)
14.Evaluate 
Ans.
15.Find that modulus and argument 
Ans.
16.For what real value of x and y are numbers equal (1+i) y2 + (6+i) and (2+i) x
Ans.(1+i) y2 + (6 + i) = (2 + i) x
y2 + iy2 + 6 + i = 2x + xi
(y2 + 6) + (y2 + 1) i = 2x + xi
y2 + 6 = 2x
y2 + 1 = x
y 2 = x – 1
x – 1 + 6 = 2x
5 = x
17.If x + iy = 
Ans.
taking conjugate both side
x2 + y2 = 1
Proved.
18.Convert in the polar form 
Ans.
19.Find the real values of x and y if (x - iy) (3 + 5i) is the conjugate of – 6 – 24i
Ans.
(x – iy) (3 + 5i) = - 6 + 24i
3x + 5xi – 3yi – 5yi2 = - 6 + 24i
20.If 
Ans.If 
6 Marks Questions
1.If z = x + i y and w = 
Show that |w| = 1 
Ans. w = 
2.Convert into polar form 
Ans.
Since Re (z) < o, and Im (z) > o
3.Find two numbers such that their sum is 6 and the product is 14.
Ans.Let x and y be the no.
x + y = 6
xy = 14
4.Convert into polar form 
Ans.
5.If α and β are different complex number with |β| = 1 Then find 
Ans.
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