### Resource Centre Mathematics

Resource Centre Mathematics Mathematics worksheet, mathematics basic points and formulas, mathematics lesson plan, mathematics multiple choice questions Workplace Dashboard CBSE Syllabus For Session 2023-24 For  :   Classes IX & X    |   Classes XI & XII Watch Videos on Maths Solutions CLASS IX MATHEMATICS FORMULAS &  BASIC CONCEPTS

## Math Assignment  Class XI  Ch - 05COMPLEX NUMBERS

Extra questions of chapter 05 COMPLEX NUMBERS class 11  with answers and  hints to the difficult questions, strictly according to the CBSE & DAV Board syllabus. Important and useful math. assignment for the students of class 11

## COMPLEX NUMBERS (XI)

Strictly according to the CBSE and DAV Board

Express the following complex number in a + ib form

Question1:  i+ i10 + i11 + i12.

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

Question 3: (2 + 3i) (2 - 3i)(1 + i2)

Question 4:

Question 5:

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

Answer: x = 3, y = -1

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

Question 8: Find the conjugate of

Question 9:

Answer: x = 0, y = -2

Question 10:

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

Question 12:

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

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:

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.

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

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