RD Sharma Class 11 Chapter 13 Solutions (Complex Numbers)
RD Sharma Class 11 Maths Solutions Chapter 13 are arranged to assist you to learn adequately all the concepts of Complex numbers. In this chapter, you get to learn what exactly are complex numbers (an amalgamation of imaginary part and real part), how to represent them, application of the complex numbers, how to locate these on the plane, what are complex equations, what is the difference between real numbers and complex numbers and many more related topics.
Above mentioned topics are comprehensively covered in 36 questions (sub-parts not counted) in 4 exercises 13.1, 13.2, 13.3 and 13.4. The simplicity of the questions varies from just evaluating the numbers to equating real and imaginary parts and also proving different equations concerning complex numbers.
You will find all the RD Sharma Class 11 Maths Solutions in plangent with their ability. Also, this will help you practice time management, which is much needed in the stressful exam environment. It’s highly recommended that you practice and solve these exercises before your school exams. The solution you get here will not only assist you with CBSE exams but also in all other competitive exams.
Topics covered in RD Sharma Solutions for Class 11 Chapter 13 Complex Numbers
Introduction to complex numbers
The numbers which have an imaginary part attached to them along with their real parts are actually complex numbers. Any of the parts can be zero. So basically complex numbers have two different kinds of information attached to them.
If ‘x’ is the real part and ‘y’ represents the imaginary part, then the complex number is written as z = x + iy where I mean iota which is a square root of negative unity.
Representation of Complex Number
Complex numbers can be represented in a lot of ways, some of the most common ways are:
- Vector form
- Trigonometric or polar form
- Cartesian or algebraic or rectangular form
- Exponential form
What is the form a + ib?
As discussed complex numbers are represented in different ways.
X = a + ib is the algebraic form, ‘a’ represents the real part and ‘b’ represents the imaginary part.
When two reciprocated perpendicular axes can be used to locate any point on the complex point of the plane. The real part is represented by the horizontal axis while the imaginary part is represented by the vertical axis.
Are all Real Numbers are Complex Numbers?
As already mentioned, Complex number has two parts, the imaginary part and the real part. that is, z = x + iy.
If y = 0, z = x which will be called as the Purely Real Number.
And if x = 0, z = iy which will be called as the Purely Imaginary Number.
Thus, it can be said that all the real numbers are also complex numbers if the imaginary part is zero.
What are Complex Equations?
The equation that involves complex numbers in them is known as the complex equation.
For example1: z = (5+9i) (6+4i)
In the given example, z is a multiple of two complex numbers. When we multiply these complex numbers we can get the value of z.
For example1: x2 + 2x + 5 = 0
Example 2 is also an example for complex equations, which can have any complex number as the solution.
Discussion Exercises of RD Sharma Solutions for Class 11 Chapter 13 Complex Numbers
- Out of the four exercises (13.1 to 13.4) of this chapter, the first exercise has easy questions like evaluating the numbers by simplifying them or finding the values of x and y. Going forward with the exercises, questions become complicated as they include harder topics like What is I in math?, What is the form a + ib? and Can we take the square root of a negative number? etc.
- These questions are perfectly in line with the class 11 syllabus, So, therefore, it gives students an idea about the kind of questions that can be asked in the exam.
- Along with improving student’s time management skills in an exam, these questions also boost their analytical skills.
- Complex Numbers are not limited to math textbooks only, they have extensive applications in diverse scientific and associated areas such as cartography, quantum mechanics, electromagnetism, fluid dynamics, vibration analysis, and control theory.
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