How is a complex number ever a real number?

Question

For my final exam, I have to know why a complex number CAN be a real number. Which cases can a complex number be a real number? I thought that it couldn't, but I know I'm incorrect. Help?

Answer 1

When it doesn't have an imaginary part.



Your question is rather like asking "How is an integer ever an even number?" The answer of course is that all even numbers are integers too, even though the converse isn't necessary true. Likewise, complex numbers INCLUDE both real and imaginary numbers. A complex number is any number can than be written in the form of a + bi, where a and b are real. So a number like "5" is a complex number because you can write it as 5 + (0*i).

Answer 2

A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1.

In the special case where b=0, a+0i=a. Hence every real number is also a complex number.



And in the special case where a=0, we call those numbers pure imaginary numbers.

Note that 0=0+0i, therefore 0 is both a real number and a pure imaginary number.



Do not confuse the complex numbers with the pure imaginary numbers.

Every real number is a complex number and every pure imaginary number is a complex number also.

Answer 3

The complex number a + ib has a real part and an imaginary part. A is the real part and b is the imaginary part. If the imaginary paart is zero (b=0) then the complex number a + ib = a, a ral number.



Every real number is complex and some complex numers are real. If x is any rela number then it tis the complex number x + i*0

Answer 4

I think it's a bit of a trick question. If a complex number is real, then the complex part would be zero. For example, 3 +2i.



Hope this helps!

Answer 5

A complex number is in the form of a+bi. Therefore, it is real when the coefficient of the imaginary number, or b, is equal to 0.

Answer 6

a complex number is a+bi, with a and b real. if b were 0, then you have a+0i =a, which is real.

Answer 7

on account that authentic numbers are complicated too (their imaginary section is 0i) you've been doing complicated type math because you've been 5. they're really ordinary btw, they merely inform you that the sq. root of -a million is i and then you stick with each and every thing you recognize from common authentic algebra.