Determine the value of a if (√3 + ai)/(1 - √3i) is a real number, and find this number. The answer they gave is a = 3 and the real number is √3.
If (√3 + ai)/(1 - √3i) is a real number, then doesn't it mean that (√3 + ai)/(1 - √3i) is x in x + yi? So, is it correct to rearrange it in this way,
(√3 + ai)/(1 - √3i) + yi = z
But then, if I arranged it in that way, I cannot see any possible way to find "a". Can you help me? Thanks.
Oh, thanks people! Many mighty thanks. Huh...should have asked you guys before I wasted half of my pen's ink on this question. Thanks again, dudes! By the way, what does it mean by (√3 + ai)/(1 - √3i) is a real number? If what you guys did above is true ( which I believe it really is) then, wouldn't it make (√3 + ai)/(1 - √3i) a complex number but not a real number? Because if it was a real number, then the equation (√3 + ai)/(1 - √3i) + yi = z would have been correct, right? Sorry, as you can see my tag name, I'm a newbie in polynomials.
And, the Abstractionist,
(a + 3)/4 = 0
a = -3
Why do I have to set the imaginary part to 0? Is there any condition that I missed out?
in general we write the complex number like
when we say
real number that's mean the factor of i should be zero because if we have a factor instead of zero that mean it is not a real number it is imaginary I think you know that
for example if they ask you is
real you should simplify make no i in the denominator bu multiply it with
like that we remove i from the denominator you will see that it is not a real because we find i in the number try to evaluate it
I think it is clear now