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# fp1 complex numbers

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1. not related to OP but I also have a complex number question:
(i) Expand and simplify where a and b are real numbers, and i is

I got
which simplified to

(ii)Deduce that if is real then either or

I understand b=0, because that would make all of the terms with b as a factor, which includes all of the terms with i, 0. But I have no idea how to do the second one.
2. (Original post by Shipreck)
not related to OP but I also have a complex number question:
(i) Expand and simplify where a and b are real numbers, and i is

I got
which simplified to

(ii)Deduce that if is real then either or

I understand b=0, because that would make all of the terms with b as a factor, which includes all of the terms with i, 0. But I have no idea how to do the second one.
If it is real, then the imaginary part of the complex number would be zero, i.e . This means that either or giving the second required result.
3. (Original post by Shipreck)
not related to OP but I also have a complex number question:
(i) Expand and simplify where a and b are real numbers, and i is

I got
which simplified to

(ii)Deduce that if is real then either or

I understand b=0, because that would make all of the terms with b as a factor, which includes all of the terms with i, 0. But I have no idea how to do the second one.
You expanded correctly. Since you are convinced that b=0 will make it real, look at the imaginary part of the expansion and make it equal 0. Divide that equation through by b (assuming its not 0) and there you have it. The post above me would get you both solutions at once by means of factorising out the b rather than dividing which is more useful than by looking at the expanded and factorised forms separately.
4. (Original post by Shipreck)
not related to OP but I also have a complex number question:
(i) Expand and simplify where a and b are real numbers, and i is

I got
which simplified to

(ii)Deduce that if is real then either or

I understand b=0, because that would make all of the terms with b as a factor, which includes all of the terms with i, 0. But I have no idea how to do the second one.
If is real, then the imaginary part is 0 i.e. in .

Hence we can factorise the expression: . I'm sure you can now see we get and .
5. (Original post by RDKGames)
You expanded correctly. Since you are convinced that b=0 will make it real, look at the imaginary part of the expansion and make it equal 0. Divide that equation through by b (assuming its not 0) and there you have it. The post above me would get you both solutions at once by means of factorising out the b rather than dividing which is more useful than by looking at the expanded and factorised forms separately.
(Original post by NeverLucky)
If is real, then the imaginary part is 0 i.e. in .

Hence we can factorise the expression: . I'm sure you can now see we get and .

(Original post by AMarques)
If it is real, then the imaginary part of the complex number would be zero, i.e . This means that either or giving the second required result.
Thank you. I don't know how I didn't see that. I'm such an idiot XD.

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