Further maths complex numbers

How do show (a+bi)/(a-bi) = c+di and then prove c^2 + d^2=1
Do I realise the denominator first but then what do I do thanks

How do show (a+bi)/(a-bi) = c+di and then prove c^2 + d^2=1
Do I realise the denominator first but then what do I do thanks

Yes, you need to make the denominator real by multiplying by the complex conjugate.
Having done so, you need to group real and imaginary terms to label c and d.
Once you've done that a minor computation yields the final result.

Ok I have got (a^2+2abi-b)/(a^2+b) how would I simplif?y this would it be 1-1+2abi I think thus is wrong can you please help? Thankyou

Is that: $\dfrac{a^2-b^2+2abi}{a^2+b^2}$?
Because if so you are essentially done, you just need to break the fraction into real and imaginary parts, and equate them to c and d.