Math, asked by Rizwanbozdar, 3 months ago

1+í ÷í.
í stands for iota​

Answers

Answered by varadad25
9

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\:}}}}

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