Math Assignment Class XI Ch-04 | Complex Numbers

 Math Assignment  Class XI  Ch - 04

Extra questions of chapter 04 COMPLEX NUMBERS class 11  with answers and  hints to the difficult questions, strictly according to the CBSE & DAV Board syllabus. 

ASSIGNMENT ON COMPLEX NUMBERS (XI)

Strictly according to the CBSE and DAV Board

Express the following complex number in a + ib form

Question1:  i⁹ + i¹⁰ + i¹¹ + i¹².

Answer: 0 + 0i

Question 2:  (7 - 2i) - (4 + i) + (- 3 + 5i)

Answer: 0 + 2i

Question 3: (2 + 3i) (2 - 3i)(1 + i²)

Answer: 0 

Question 4:   

Evaluate:  

Answer: 

Question 5: 

Evaluate:   

Answer: -1 + 0i 

Question 6:  If 3 + yi - 2i = x - i. Find y.

Answer: x = 3, y = 1

Question 7: Find the modulus of (1 - i)¹⁰.

Answer:  32

Question 8: Find the conjugate of  

Answer: 

Question 9: 

Answer: x = 0, y = -2

Question 10: 

Evaluate:  2x³ + 2x² - 7x + 72,  when   

Answer:  4

Solution Hint  

2x = 3 - 5i

2x - 3 = - 5i

Squaring on both side and arranging all terms on the one side of equal we get

2x² - 6x + 17 = 0 ...... (i)

Now divide the given cubic equation by eqn. (i) we get quotient = x+4 and remainder = 4

2x³ + 2x² - 7x + 72 = (2x² - 6x + 17)(x + 4) + 4

                            = 0 × (x + 4) + 4

                            = 4

Question 11: Evaluate: x⁴ + 4x³ + 6x² + 4x + 9,   where  x = -1+ i√ 2

Answer:  12 

Question 12: 

If z = 2 - 3i, then show that z² - 4z + 13 = 0. Hence, find the value of 4z³ - 3z² + 2z + 170.

Answer: 5 - 6i

Question 13:

Find the real values of x and y if     is the conjugate of  5 - i

Answer: x = 4, y = 6

Question 14: Evaluate:   

Answer: 28i

Question 15: Find two real numbers x and y if (x – iy) (3 + 5i) is the conjugate of  – 6 – 24i.

Question 16: Write the conjugate of complex number  in the form a + ib. 

Answer:   

Question 17: If x + iy=    ,  then find the value of x² + y².

Answer:  x² + y² =   

Question 18: If (x - iy)^1/3 = a +ib,  x, y, a ∊ R, then  show that    

Question 19: If (x + iy)³ = u + iv, then show that   

Question 20: If     , then show that 4p² + q² =1 

Question 21: Evaluate :    , n ∈ N, where   

Answer: i

Solution Hint: 

 

     = i¹(1 + i) + i²(1 + i) + i³(1 + i) + i⁴(1 + i) + ……… 13 terms

     = i

Question 22: If (1 + i)(1 + 2i)(1 + 3i)......(1 + ni) = a + ib . Prove that 2.5.10.....(1+ n² ) = a² + b².

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FOLLOWING QUESTIONS ARE DELETED FROM CBSE SYLLABUS

Question 19: 

Express the complex numbers in standard form and hence convert it in polar form.

Answer: Z = 0 - 2i

Polar form is :  

Question 20:

Convert the complex number 2 - 2i into polar form. Also write its argument.

Question 21: Find the square root of the complex number 4 - 4√3i

Question 22:  Find the square root of  Z =  

Question 23: Convert the complex number      into polar form.

Question 24: Find principal argument of the complex number 

Answer:   

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