Question

simplify a+ib by a-ib+ a-ib by a+ib

Answer 1

Answer :

Now,

(a+ib)/(a-ib) + (a-ib)/(a+ib)

= {(a + ib)(a + ib)}/{(a - ib)(a + ib)}
+ {(a - ib)(a - ib)}/{(a + ib)(a - ib)}

= (a² + 2iab + i²b²)/(a² - i²b²)
+ (a² - 2iab + i²b²)/(a² - i²b²)

= (a² + 2iab - b² + a² - 2iab - b²)/(a² + b²),
since i² = - 1

= (2a² - 2b²)/(a² + b²)

= 2(a² - b²)/(a² + b²),

which is the required simplified form.

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