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# Further maths complex numbers watch

1. 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
2. (Original post by Bobby21231)
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.
3. (Original post by Bobby21231)
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
Taking the modulus of both sides is the quickest way
4. (Original post by joostan)
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
5. (Original post by Bobby21231)
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: ?
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.
6. (Original post by joostan)
Is that: ?
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.
Ok thankyou very much for your help

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