Class 12 Mathematics Complex Number Notes has been updated according to the latest syllabus of 2080. It means the solutions of Complex Number chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of Complex Number because we are here to serve you.

## Chapter – 3

__Complex Number__

A complex number is a number that combines a real part and an imaginary part. It is typically expressed in the form a + bi, where “a” and “b” are real numbers, and “i” is the imaginary unit (√-1). The real part represents the horizontal axis on the complex plane, while the imaginary part represents the vertical axis.

Complex numbers are used in various mathematical calculations, such as solving equations that have no real solutions, electrical engineering, signal processing, and quantum mechanics. They provide a powerful tool for representing and manipulating quantities that involve both real and imaginary components.

Class 12 Complex Number chapter has 2 exercises in total. You can click on the buttons given below to view exercise-wise notes.

### Application of Complex Number

Complex numbers find applications in various fields beyond mathematics. In physics, they are used to describe alternating current circuits, quantum mechanics, and wave functions. In engineering, complex numbers are utilized in signal processing, control systems, and impedance calculations.

Moreover, in economics and finance, complex numbers play a role in modeling oscillations and fluctuations. The versatility of complex numbers extends their utility far beyond theoretical mathematics, making them a valuable tool in solving practical problems across different disciplines.

## Class 12 Mathematics Complex Number Notes PDF

This PDF will provide the solutions of every question from the 2nd exercise of class 12 complex number. If you want the solutions of other exercises then you can select the exercise from the button given above.

## Which of the following is a complex number?

- a) 3 + 4i
- b) √9
- c) -5
- d) 2/3

**Correct Answer: a) 3 + 4i**

**Explanation:** A complex number is typically expressed in the form a + bi, where “a” and “b” are real numbers and “i” is the imaginary unit (√-1). In this form, the real part is “a” and the imaginary part is “bi. In the given options:-

**Option a)**3 + 4i is a complex number with both a real part (3) and an imaginary part (4i).**Option b)**√9 = 3 is also a real number without an imaginary part.**Option c)**-5 is a real number without an imaginary part.**Option d)**2/3 is a real number without an imaginary part.- Therefore, the correct answer is
**option a)**3 + 4i, as it meets the criteria of being a complex number with both real and imaginary components.

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