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Important Questions for CBSE Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

 



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, zare 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)= 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

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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