In This Post we are providing Chapter-5 COMPLEX NUMBERS AND QUADRATIC EQUATIONS NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.
NCERT MOST IMPORTANT QUESTIONS ON COMPLEX NUMBERS AND QUADRATIC EQUATIONS
1. Evaluate i-39
Ans.
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image001.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image002.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image003.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image004.png)
2. Solved the quadratic equation
Ans.
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image007.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image008.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image009.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image010.png)
3. If = 1, then find the least positive integral value of m.
Ans.
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image013.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image014.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image015.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image016.png)
4. Evaluate (1+ i)4
Ans.
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image018.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image019.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image020.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image021.png)
5. Find the modulus of
Ans. Let z =
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image023.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image024.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image025.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image026.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image027.png)
6. Express in the form of a + ib. (1+3i)-1
Ans.
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image029.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image030.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image031.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image032.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image033.png)
7. Explain the fallacy in -1 = i. i. =
Ans. is okay but
is wrong.
8. Find the conjugate of
Ans. Let z =
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image038.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image039.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image040.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image041.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image042.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image043.png)
9. Find the conjugate of – 3i – 5.
Ans. Let z = 3i – 5
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image044.png)
10. Let z1 = 2 – i, z2 = -2+i Find Re
Ans. z1 z2 = (2 – i)(-2 + i)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image046.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image047.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image048.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image049.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image050.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image051.png)
11. Express in the form of a + ib (3i-7) + (7-4i) – (6+3i) + i23
Ans. Let
Z =
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image053.png)
12. Find the conjugate of
Ans.
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image056.png)
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
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image058.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image059.png)
![](https://cdn1.coolgyan.org/images/static/impq/11/maths/ch05/1m/image060.png)