Question

express in the form of a+ib 1/1+i​

Answer 1

Step-by-step explanation:

First of all we have to write its denominator as a+bi.

So,

$\frac{1}{1 + i} = \frac{1}{a + bi}$

where, a = b = 1

Now,

We have to rationalize the dinominator.

$hence \: \frac{ 1 }{a + bi} \times \frac{a - bi}{a - bi}$

$\frac{a - bi}{ {a}^{2} - {(bi)}^{2} }$

$= \frac{a - bi}{ {a}^{2} + {b}^{2} }$

Now we can split it as following:

$= \frac{a}{ {a}^{2} + {b}^{2} } - \frac{bi}{ {a}^{2} + {b}^{2} }$

Now substituting the value of a and b on the above expression i.e. a = b = 1

$= \frac{1}{ {1}^{2} + {1}^{2} } - \frac{1i}{ {1}^{2} + {1}^{2} }$

$= \frac{1}{2} - \frac{1}{2} i$

$= ( \frac{1}{2} ) + ( - \frac{1}{2})i$

Hence solved

The question was difficult enough to take this much time. Sorry for that.

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