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ElenaW [278]
2 years ago
6

Write the quotient 13/5 - i in the form a + bi .

Mathematics
1 answer:
Ray Of Light [21]2 years ago
8 0
<h3><u>Given Quotient:- </u></h3>

\red{➤}\:\sf \dfrac{13}{5-i}

\\

<h3><u>To Do:-</u></h3>

\orange{☛}\:\sf Write \: given \: Quotient  \:in \: a+bi  \:form

\\

<h3><u>Solution:-</u></h3>

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{13}{5-i} \\\end{gathered}

Multiplaying denominator and numerator by 5+i to get denominator as real number

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{13(5+i)}{5-i(5+i)} \\\end{gathered}

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{5^2-i^2} \\\end{gathered}

\quad\quad\quad\quad\quad\sf ((a+b)(a-b)=a^2-b^2)

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{25-(-1)} \\\end{gathered}

\quad\quad\quad\quad\quad\sf (For\:Complex\: Number,i ; i^2 = -1)

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{25+1} \\\end{gathered}

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{26} \\\end{gathered}

\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{\cancel{65}}{\cancel{26}}+\frac{\cancel{13}i}{\cancel{26}}  \\\end{gathered}

\begin{gathered}\\\quad\longrightarrow\quad\boxed{\sf {\frac{5}{2} +\frac{1}{2} i}}\\\end{gathered}

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