Question

If a2 + b2 = 1. Then
1+b+ia
1+b-ia​

Answer 1

Answer:

$\frac{1+b+ia}{1+b-ia}=b+ia$

Step-by-step explanation:

Given:

$a^2+b^2=1$

$(b+ia)(b-ia)=1$

$\implies\bf\,b-ia=\frac{1}{b+ia}$.........(1)

Now,

$\displaystyle\frac{1+b+ia}{1+b-ia}$

$=\displaystyle\frac{1+b+ia}{1+\frac{1}{b+ia}}$ (using (1))

​$=\displaystyle\frac{1+b+ia}{\frac{1+b+ia}{b+ia}}$

$=\displaystyle\frac{1+b+ia}{1+b+ia}(b+ia)$

$=b+ia$

$\implies\boxed{\bf\frac{1+b+ia}{1+b-ia}=b+ia}$

Answer 2

Answer:

step by step explained in the images.

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