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### Math Assignment Class XI Ch-04 | Complex Numbers

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## 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. **

**MATHEMATICS ASSIGNMENT ON **

**COMPLEX NUMBERS (XI)**

**Strictly according to the CBSE and DAV Board**

**Question1: i**

^{9 }+ i^{10 }+ i^{11 }+ i^{12}.**Answer: 0 + 0i**

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

**Answer: 0 + 2i**

**Question 3: (2 + 3i) (2 - 3i)(1 + i**

^{2})**Answer: 0 **

**Question 4:**

**Answer: **

**Question 5:**

**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:**

**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**

**2x ^{2} - 6x + 17 = 0 ...... (i)**

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

**2x ^{3} + 2x^{2} - 7x + 72 = (2x^{2} -
6x + 17)(x + 4) + 4**

**
= 0 × (x + 4) + 4**

**= 4**

**Question 11:**

**Evaluate: x**

^{4}+ 4x^{3}+ 6x^{2}+ 4x + 9, where x = -1+ i√ 2**Answer: 12 **

**Question 12:**

**If z = 2 - 3i, then show that z ^{2} - 4z + 13 = 0. Hence, find the value of 4z^{3 }- 3z^{2 }+ 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 x**

^{2}+ y^{2}.**Answer: x ^{2} + y^{2} = **

**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
**

**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: **

**Question 25:**

**Evaluate :**, n ∈ N, where

Answer: i

Solution Hint:

^{1}(1+i) + i

^{2}(1+i)+ i

^{3}(1+i)+ i

^{4}(1+i)+ ……… 13 terms

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