What is the point of multiplying by a conjugate For example for integrals , I kn

Question

What is the point of multiplying by a conjugate
For example for integrals ,
I know it’s good for getting to substitute trig identities, aside from that how will I know when to multiply by the conjugate, to make the integral be easily integrated.
Thank you What is the point of multiplying by a conjugate
For example for integrals ,
I know it’s good for getting to substitute trig identities, aside from that how will I know when to multiply by the conjugate, to make the integral be easily integrated.
Thank you
For example for integrals ,
I know it’s good for getting to substitute trig identities, aside from that how will I know when to multiply by the conjugate, to make the integral be easily integrated.
Thank you

Explanation / Answer

Multiplying and dividing by any number makes no change in the given quantity.

This means when we multiply and divide by conjugate we make no change in the quantity .well the question arises why we do so.well ! We multiply by conjugate to rationalise the denominator. So that the simplification becomes easier

We use the identity (a+b)(a-b)=a2-b2

so when we use it on

(a+ib)(a-ib)=a2--i2b2

=a2+b2   [ because i2=-1]

Observe how a complex quantity gets reduced to a rational number upon multipkyingvit with its conjugate.

Which actually simplifies or

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