Complex Number Class 12 Mathematics 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. The imaginary part is a multiple of the imaginary unit “i,” which is the square root of -1.

Complex numbers are written in the form a + ib, where “a” represents the real part and “ib” represents the imaginary part. These numbers are used in various mathematical calculations and have applications in fields like engineering, physics, and more.

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

### Polar Form of a Complex Number

Let z = (x, y) =x+ iy be a complex number. It can be represented by a point P in the complex plane with cartesian coordinates (x, y) Let 0 be the angle in the standard position with OP as its terminal arm, and the length of the line segment OP.

x = rcosθ y = rsinθ

Thus, the complex number, z = x + iy may be written in the following trigonometric form (polar form) z = r(cos θ + isinθ)

## Complex Number Class 12 Mathematics Notes PDF

This PDF will provide the solutions of every question from the 1st 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 not a Complex Number?

- 5 + 3i
- -2
- √7
- 4i

**Correct Answer: b) -2**

**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)**5 + 3i is a complex number with both a real part (5) and an imaginary part (3i).**Option c)**√7 is also a complex number as it can be written as √7 + 0i, where the real part is √7 and the imaginary part is 0.**Option d)**4i is a complex number with an imaginary part (4i) and a real part of 0.- However,
**option b)**-2 is not a complex number as it lacks an imaginary part. Complex numbers must have both a real and an imaginary component.

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