In mathematics, there are many Numbers one of them is imaginary number. Imaginary number definition says that it is a type of number which is always less than or equal to zero whenever it is squared. Let iy, is an imaginary number when it is added to a real number, which is x, then their addition results into a Complex Number of the form x + iy, where x and y are known as the real part and the imaginary part of that complex number.
Imaginary numbers rulesBack to Top
Complex number is a Combination of two Numbers or parts, one is real number and the other is Imaginary Number. Here the concept of imaginary number is introduced. We represent the imaginary number with ‘i’ or sometimes with ‘j’. ‘I’ is another representation of √-1. With help of imaginary number rules you can easily solve several problems related to imaginary numbers or in order to operate imaginary numbers we should follow imaginary numbers rules:
Rule 1: Imaginary number is represented by the ‘I’ which is √-1.
Rule 2: We should have the knowledge of the power on imaginary number. Let us take an example to understand it better.
i0 = 1; i1 = i; i2 = -1; i3 =i.
Rule 3: Property of conjugation: If there is a number as x + iy then its conjugate will be x – iy.
For instance, if a number is 6 + 8i so its conjugate number will be 6 – 8i. -8 stands for the y.
Rule 4: Multiplication of two imaginary numbers: We can elaborate multiplication better with an example so let’s take an example.
· We have to multiply these two numbers so first we multiply the real part of first number with the real part of another number.
· Now multiply imaginary part with other number.
· Add the real parts and the imaginary part separately.
· Add these real and imaginary parts together.
Rule 5: Power of imaginary numbers:
We solve the power as we solve in Algebra. For any number of power (x+iy)n
(a+b)2 = a2 +b2+ 2ab
Rule 6: Division by x + iy
Let us understand it with an example, say we have to divide 4 – 3i by 3 + 2i
· First multiply the numerator and the denominator with the conjugate of denominator which is 3 -2i.
· When we multiply the denominator with its conjugate we get a real value (3 +2i)(3-2i)=9 +4=13.
· In numerator, we ignore the imaginary part after the multiplication.
· After multiplication we get the real values (12+6) and we divide it in order to get the divided value 18/13 which is the result.
These are some imaginary number rules.