When we need to square the root of the negative integer, then we need to use the complex numbers or the imaginary numbers. We use simple procedures to solve the addition, subtraction, and multiplication division of complex numbers. The absolute value calculator can be used at calculatored.com to find the addition, subtraction, multiplication, and division of complex numbers.
What is a complex number?
First, we need to understand the complex number, The complex is the square root of a negative integer and we represent it as:
i = -1 were i2= -1
Now we know that the “ i “ is equal to the square root of the -1, and simply equal to the -1. The absolute value graph calculator makes it possible to find the graph of the complex numbers.
The standard form of the complex number:
The complex numbers can be written as:
a+bi
Where “a” is the real part of the equation and the “bi” is the imaginary portion of the complex number
| Now take the example of a number: 10 + 5i, where 10 is a real number and the 5i is its imaginary part. The Equality of Complex Numbers: We can add and subtract two complex numbers if they’re real and the complex numbers match each other: |
a+bi= c+di
Now we can add and subtract the complex numbers as their real numbers match and the imaginary numbers to each other. The absolute value equation calculator can be used to find the addition easily.
The addition and the subtraction:
| We use the simple theorem for addition and the subtraction the of the complex numbers: We are writing them as: (a+bi) +(c+di) = (a+c) +(b+d)i (a+bi) -(c+di) = (a-c) +(b-d)i |
We are adding and subtracting the real numbers separately from the complex numbers and this makes the whole question easy. The absolute value inequality calculator is easy to use.
| Example of addition: Now to add two complex numbers, (7+2i)+(9+5i)Now we add the real numbers together and the imaginary number separately:(7+9)+(2+5)i= 16+7i We can use the absolute value calculator to find the values of the complex numbers.Example of subtraction: Now to subtract two complex numbers, (-1-i) – (8-2i)Now we subtract the real numbers together and the imaginary number separately:(-1-8)+(-1+2)i= -9+i We can use the absolute value inequalities to find the values of the complex numbers. |
Multiplication of Complex Numbers:
Now to multiply an expression we use:
Supplication of the expression:
-2i (5+3i)
We get the answer:
-10i- 6i2
As i2= -1
-10i- 6(-1)
We get
-10i+6
The standard form:
In the standard form where the real number is at first the imaginary at the second place, we got
a+bi
We got
The final answer =6- 10i
To find the multiplication answer of two complex numbers we can use the absolute value equations calculator and solve the answer easily.
Division of the complex number:
For division, we follow these steps:
The conjugate of the denominator:
We first find the conjugate of eh denominators by changing the signs of the denominator:
(a+bi) and (a-bi) are conjugates of each other
Multiplication with the denominator and numerator of fraction:
Now multiply the fraction with the exact conjugate
We get the answer in the form
(a+bi) (a-bi) = a2+ b2
Now add the real numbers with each other and the imaginary numbers separately and i2multiply it with -1, by definition:
And then write down the answer in the standard form as in the multiplication we have done, we can use the absolute value inequality calculator to find the division of the complex numbers.