Answer
385.8k+ views
Hint:Complex term can be treated as algebraic variables, but the thing is the properties used here are a bit different, all calculations can be done like for variables, in the final answer only you can have to put the predefined values of complex numbers, rest everything is same and if applicable certain properties are needed to be used.
Formulae Used:
\[{a^2} - {b^2} = (a + b)(a - b)\]
Complete step by step answer:
The given complex term is \[\dfrac{{5 - i}}{{5 + i}}\]. Here we have to multiply the term in numerator and denominator with the conjugate of denominator such that we can proceed further to obtain the best possible solution for the question, on solving we get:
\[\dfrac{{5 - i}}{{5 + i}} \times \dfrac{{5 - i}}{{5 - i}} \\
\Rightarrow \dfrac{{{{(5 - i)}^2}}}{{{5^2} - {i^2}}}\left( {using\,the\,formulae\,{a^2} - {b^2} = (a + b)(a - b)} \right) \\
\Rightarrow \dfrac{{{5^2} + {i^2} - 10i}}{{25 - ( - 1)}} \\
\Rightarrow \dfrac{{25 + ( - 1) - 10i}}{{26}} \\
\Rightarrow \dfrac{{25 - 10i}}{{26}} \\
\therefore \dfrac{{25}}{{26}} - \dfrac{{10}}{{26}}i \]
This is the final required solution for the given term, since here no further simplification can be done hence it is the simplest possible answer.
Additional Information:
Here we can multiply and divide with the conjugate of numerator also but by using that we can’t separate the real and complex term into two fractions, as we did. Because the complex part will come under a denominator and then separation can’t be done.
Note: For the question in which simplification is needed, then for such questions you need to think that how you can obtain the simplest form of the equation, like for here we have to separate the real and complex term, so accordingly we think about the steps and get the required best possible solution for the question.
Formulae Used:
\[{a^2} - {b^2} = (a + b)(a - b)\]
Complete step by step answer:
The given complex term is \[\dfrac{{5 - i}}{{5 + i}}\]. Here we have to multiply the term in numerator and denominator with the conjugate of denominator such that we can proceed further to obtain the best possible solution for the question, on solving we get:
\[\dfrac{{5 - i}}{{5 + i}} \times \dfrac{{5 - i}}{{5 - i}} \\
\Rightarrow \dfrac{{{{(5 - i)}^2}}}{{{5^2} - {i^2}}}\left( {using\,the\,formulae\,{a^2} - {b^2} = (a + b)(a - b)} \right) \\
\Rightarrow \dfrac{{{5^2} + {i^2} - 10i}}{{25 - ( - 1)}} \\
\Rightarrow \dfrac{{25 + ( - 1) - 10i}}{{26}} \\
\Rightarrow \dfrac{{25 - 10i}}{{26}} \\
\therefore \dfrac{{25}}{{26}} - \dfrac{{10}}{{26}}i \]
This is the final required solution for the given term, since here no further simplification can be done hence it is the simplest possible answer.
Additional Information:
Here we can multiply and divide with the conjugate of numerator also but by using that we can’t separate the real and complex term into two fractions, as we did. Because the complex part will come under a denominator and then separation can’t be done.
Note: For the question in which simplification is needed, then for such questions you need to think that how you can obtain the simplest form of the equation, like for here we have to separate the real and complex term, so accordingly we think about the steps and get the required best possible solution for the question.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)