Find a condition so that the given complex numver is real.We use the conjugate

When dealing with complex number one needs to know the definition of the conjugate of a complex number ; we have already defined that and we have also shown that in one of the previous videos . We're going to use the concept of the conjugate to prove that this number here is real. If only if is if only if the complex number is pure imaginary we could have used the algebraic form of the complex number and solve this problem. But this one would definitely take a lot of time. Because the in this case we would have to do more algebra, but in our solution we have used the concept of the conjugate .

That says that if the conjugate of a complex number is equal to itself that means the number is real. So that's what we have used. And that's what we have proved. We will add more videos concerning calculus , algebra , geometry, differential equation , numerical analysis and more algorithm computations and animations in the next videos.
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