Mathematics: What are the steps to simplify the expression 5+i/1+i

What are the steps to simplify the expression 5+i/1+i

Ответ:

smithsa10630

14.03.2022

I assume you mean

$\dfrac{5 + i}{1 + i}$

although what you wrote means something else.

To get rid of the imaginary part in the denominator, you must multiply this fraction by a fraction which is the complex conjugate of the denominator over itself.
The denominator of the original fraction is 1 + i.
Its complex conjugate is 1 - i.
Multiply the original fraction by

$\dfrac{1 - i}{1 - i}$

Now we'll do it.

$\dfrac{5 + i}{1 + i} \times \dfrac{1 - i}{1 - i} =$

$= \dfrac{(5 + i)(1 - i)}{(1 + i)(1 - i)}$

$= \dfrac{5 - 5i + i - i^2}{1 - i^2}$

$= \dfrac{5 - 4i - (-1)}{1 - (-1)}$

$= \dfrac{6 - 4i}{2}$

= 3 - 2i

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Ответ:

anggar20

26.05.2023

Mathematics

the answer is 521

Step-by-step explanation: i don't know how i got it i am a human calculator :)

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What are the steps to simplify the expression 5+i/1+i

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