This is because, we define:Īll imaginary numbers, when squared, give a negative real number. So is a negative number times itself! So it may seem that no number can satisfy this property! In fact no real number (a number in the real number system which is what you are used to working with), satisfies this property - only imaginary numbers do. Well a positive number times itself is a positive number. Try to think of a number that when multiplied by itself, gives a negative number. It opens up a whole new number system called the imaginary numbers. So, in summary, real numbers and imaginary numbers are both specical kinds of complex numbers:Ġ + bi is the form of an imaginary number ![]() NOTE: far too many teachers and textbooks get this wrong and call all nonreal numbers "imaginary numbers", so you need to check with your teacher to make sure you use the terms the way the teacher wants, even if it is wrong. This means that an imaginary number is a number that can be expressed is i times some real number other than 0. In other words, an imaginary number can be written as 0 + bi. As the name implies, all numbers that are not real numbers are nonreal complex numbers.Īn imaginary number is a nonreal number which, when written in the a + bi form, the a IS 0. Thus, a real number is a special kind of complex number, specifically one in which the coefficient (b) of i is 0 when written in a+bi form.Ī nonreal complex number (often just called a nonreal number) is a complex number which, when written in the form of a + bi, the b is NOT 0. All real numbers can be expressed in terms of a + 0i. A complex number is a number that can be written (that doesn't mean it is currently being expressed this way) as a + bi, where a and b are real numbers.Īt least in terms of numbers you will encounter at this level of study, this means that ALL numbers are complex numbers because all numbers can be expressed in the form of a + bi.Ī real number is either a rational or irrational number.
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