Concepts of Modulus of a Complex Number:- If you have read something about modulus, then there are different questions associated with it. In mathematics, there are different types of numbers and we know about it. So, when it comes to defining a Modulus of a complex number, many students get confused. Those who don’t know about the same must understand that in an argand plane there is an origin. And the distance between the complex number and the origin is called the modulus of the complex number. For instance, the complex number is z = x + iy.
In this, x and y are real and in which ‘i’ is an imaginary part with the value of √-1. If this is the case then the non-negative value √(x2 + y2) will be considered as the modulus of the complex number (z = x + iy). Remember that this same mathematics contains modules like geometry where students calculate the radius of a circle. Coming back to the modulus part, let us discuss some vital points about the modulus of a complex number. Here we go!
Introduction to Complex Numbers (Concepts of Modulus of a Complex Number)
In mathematics, you are dealing with several numbers. One type of such numbers are complex numbers. They are the numbers that are mathematically expressed in the a+ib form. In such mathematical representation, ‘i’ is an imaginary part also known as iota having the value of (√-1). And a and b are real numbers that are like other normal numbers. For example, it can be 22+33i.
How can you Find the Argument and the Modulus of a Complex Number?
If you want to find the argument and modulus of a complex number easily, there are certain steps you need to follow. Here are those!
- Step 1: Draw the graph of the complex number to check whether the complex plane is there in it or not. It will help you later in determining the argument.
- Step 2: Step 2: Calculate the modulus of a complex number z = x + iy. To accomplish this task use the formula |z|= the square root of a2+b2
- Step 3: Finally, to calculate the argument of the same complex number you need to put the formula of tan inverse. Thus, if the complex number is z = a + ib, use the formula of arg (z) = tan-1 (b/a). Then, you need to adjust your result on the graph found. Remember the argument range should be (−π,π].
Important Notes for students about the Modulus of Complex Number
- The complex number distance is depicted as a point in the argand plane (a,b) from the origin of the graph (0,0). It will be known as the modulus of a complex number.
- If the complex number is zero then the ultimate value of the modulus will also be zero.
- The modulus of a complex number a + bi is similar to the vector magnitude of the same complex number.
- The sum of squares or real and imaginary parts of a complex number and their square root will be considered as the modulus of a complex number.
Remember that the modulus of a complex number can be derived with the help of a Pythagoras theorem. To make this task possible the hypotenuse will be represented as the modulus, base as the real part and altitude of the right triangle as an imaginary part. The modulus of a + bi will be equal to the length (or magnitude) of the vector representing a + bi.
Students should have their fundamentals strong and on tips. It is recommended for them to refer different learning materials. Gain some valuable insights and then start solving questions.
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