Table of Contents
What Are Imaginary Numbers?
Imaginary Numbers – Definition:
Imaginary numbers are a mathematical concept that were first proposed by the mathematician René Descartes in the 17th century. They are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of negative one.
Imaginary numbers are used to solve problems in physics and engineering, and they can also be used to help explain certain phenomena in mathematics. For example, the equation x2 + 1 = 0 has two solutions, both of which are imaginary numbers.
Imaginary Numbers Definition
An imaginary number is a number that is used in mathematics and physics that is not real. Imaginary numbers are used to solve problems in physics and to help understand the behavior of waves and other physical phenomena.
What is Complex Number?
A complex number is a number that can expressed in the form a+bi, where a and b are real numbers and i is the imaginary unit. The real part of a complex number is a, and the imaginary part of a complex number is b.
Real And Imaginary Numbers
Real numbers are numbers that can expressed as a decimal. The set of all real numbers includes the whole numbers, fractions, and decimals.
The set of all real numbers can be represented by the number line. The number line is a line that extends infinitely in both directions, with 0 at the middle. The real numbers are all the points on the number line that are not at the ends.
The set of all real numbers also includes imaginary numbers. Imaginary numbers are numbers that can expressed as a complex number. A complex number is a number that includes a real number and an imaginary number. The imaginary number usually written as i.
The set of all imaginary numbers can represented by the number line. The number line for imaginary numbers is the same as the number line for real numbers, except that the imaginary numbers are all at the ends.
Imaginary Numbers Chart
Imaginary numbers are those that are not real, and they denoted with the symbol “i”. This number is the square root of negative 1.
Addition Of Numbers Having Imaginary Numbers
The addition of numbers having imaginary numbers is very simple. Just add the real and imaginary parts of the numbers separately and then combine them.
For example, if you are adding 5 + 3i, then you would add 5 + 3 = 8 and 8i.
Subtraction Of Numbers Having Imaginary Numbers
To subtract two numbers that contain imaginary numbers, you first need to convert the imaginary numbers to real numbers. Then, subtract the two real numbers as you would any other two numbers.
For example, to subtract 3 – 5i, you would first convert 3i to 3, and 5i to 5. Then, you would subtract 3 – 5 = -2.
Multiplication Of Numbers Having Imaginary Numbers
To multiply two numbers together that contain imaginary numbers, simply multiply the real parts and multiply the imaginary parts.
For example, if you are multiplying 3 + 5i by 2 – 3i, you would multiply 3 by 2 and 5 by -3, and then add the results together.
Division Of Numbers Having Imaginary Numbers
There is no definitive answer to this question as different mathematicians may have different opinions on how to divide numbers having imaginary numbers. However, one possible way to divide numbers having imaginary numbers could be to consider the real and imaginary parts of the number separately. For example, the number 5 + 3i could considered to have two parts: 5 and 3i. The 5 would the real part of the number and the 3i would be the imaginary part.
Solved Imaginary Numbers Examples
1. Find the square root of -16.
2. Find the sum of 3 + 4i and 5 – 6i.
3. Find the product of 7 – 8i and 2 + 3i.
4. Find the quotient of 9 + 10i and 3 – 4i.
