Fact of the Day: 20/10/2021

Are all complex numbers imaginary?

Complex numbers are numbers of the form a + bi, where i is the imaginary unit (i = √1). The ‘real part’ of the number refers to a; the ‘imaginary part’ refers to b. While it may seem like all complex numbers have to be imaginary, they really don’t—some may be purely imaginary (and complex), some may be purely real (and complex), and others may be only complex. 

The number 5 + 3i, for example, has both a real and imaginary part, so it is only complex. The number 5, though, has no imaginary part, so it is considered real. It is also considered complex because it can be rewritten as 5 + 0i. The number 3i has no real part, so it is considered imaginary.  However, it is also a complex number because it can be rewritten as 0 + 3i. 

Further Exploration: Check out this Khan Academy article on complex numbers to learn more about them: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/a/intro-to-complex-numbers?modal=1

Fact Author: Ace 

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