Question

write the ex\frac{46 + i}{i}

Explanation:

Step1: Multiply numerator and denominator by \(i\)

To simplify \(\frac{46 + i}{i}\), we multiply the numerator and denominator by \(i\) to rationalize the denominator. So we have \(\frac{(46 + i)\times i}{i\times i}\).

Step2: Expand the numerator and denominator

First, expand the numerator: \((46 + i)\times i = 46i + i^2\). And the denominator: \(i\times i = i^2\). Recall that \(i^2=- 1\), so substitute \(i^2 = - 1\) into the numerator and denominator. The numerator becomes \(46i-1=-1 + 46i\) and the denominator becomes \(-1\).

Step3: Divide the numerator by the denominator

Now we have \(\frac{-1 + 46i}{-1}=\frac{-1}{-1}+\frac{46i}{-1}=1-46i\).

Answer:

\(1 - 46i\)