Question

divide 2-3i by 5-4i​

Answer 1

$\textbf{Given:}$

$\dfrac{2-3\,i}{5-4\,i}$

$\textbf{To find:}$

$\text{Simplified form of \dfrac{2-3\,i}{5-4\,i} }$

$\textbf{Solution:}$

$\text{Consider,}$

$\dfrac{2-3\,i}{5-4\,i}$

$\text{Multiply both numerator and denominator by 5+4\,i }$

$=\dfrac{2-3\,i}{5-4\,i}{\times}\dfrac{5+4\,i}{5+4\,i}$

$=\dfrac{(2-3\,i)(5+4\,i)}{5^2-(4\,i)^2}$

$=\dfrac{10+8\,i-15\,i-12\,i^2}{25-16\,i^2}$

$\text{But}\bf\i^2=-1$

$=\dfrac{10-7\,i+12}{25-16\,i^2}$

$=\dfrac{22-7\,i}{25+16}$

$=\dfrac{22-7\,i}{41}$

$=\dfrac{22}{41}-\dfrac{7\,i}{41}$

$\textbf{Answer:}$

$\bf\,\dfrac{2-3\,i}{5-4\,i}=\dfrac{22}{41}-\dfrac{7\,i}{41}$

Find more:

If a-bi/a+bi=1+i/1-i then,prove a+b=0

https://brainly.in/question/14173316

Express the complex number z = 5+i/2+3i in the form a + ib

https://brainly.in/question/6695271