Question

1+í ÷í.
í stands for iota​

Answer 1

Question:

Simplify:

$\displaystyle{\sf\:\dfrac{1\:+\:i}{i}}$

Answer:

$\displaystyle{\boxed{\red{\sf\:\dfrac{1\:+\:i}{i}\:=\:1\:-\:i\:}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\dfrac{1\:+\:i}{i}}$

We have to simplify the given expression.

$\displaystyle{\sf\:\dfrac{1\:+\:i}{i}}$

$\displaystyle{\implies\sf\:\dfrac{1\:+\:i}{i}\:\times\:\dfrac{i}{i}}$

$\displaystyle{\implies\sf\:\dfrac{i\:(\:1\:+\:i\:)}{i^2}}$

$\displaystyle{\implies\sf\:\dfrac{i\:+\:i^2}{-\:1}\:\qquad\cdots[\:\because\:i^2\:=\:-\:1\:]}$

$\displaystyle{\implies\sf\:-\:[\:i\:+\:(\:-\:1\:)\:]}$

$\displaystyle{\implies\sf\:-\:(\:i\:-\:1\:)}$

$\displaystyle{\implies\sf\:-\:i\:+\:1}$

$\displaystyle{\implies\sf\:1\:-\:i}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\dfrac{1\:+\:i}{i}\:=\:1\:-\:i\:}}}}$