Question

Simplify the expression

Answer 1

\[\frac{ -6+\iota }{ -5+\iota }\]

Answer 2

those are "i"s

Answer 3

\(\large\tt \begin{align} \color{black}{\text {u have to rationalize the denominator here}\\~\\
\dfrac{-6+i}{-5+i}\\~\\
=\dfrac{-6+i}{-5+i}\times \dfrac{-5-i}{-5-i}\\~\\
=\dfrac{30+6i-5i-i^2}{(-5)^2-i^2}\\~\\
=\dfrac{30+i+1}{25+1}\\~\\
=\dfrac{31+i}{26}
} \end{align}\)

Answer 4

bear in mind that \(\bf a^2-b^2 = (a-b)(a+b)\qquad thus
\\ \quad \\
(-5+i)(-5-i)\implies (-5)^2-(i)^2\implies 25-(i^2)\implies 25-(-1)\implies 26\)

Answer 5

Thank you so much!