MHB Is it possible to write this expression in the form $a+bi$?

[Karpthulu912]

so the karp is back with another question about math and well this time its not a long homework but rather a genuine question

is this possible?

(5-i)/i​

 

[MarkFL]

If you are asking if it's possible to write this expression in the form $a+bi$, yes, it is:

$$c=\frac{5-i}{i}$$

Let's multiply this expression by $$1=\frac{i}{i}$$:

$$c=\frac{5-i}{i}\cdot\frac{i}{i}=\frac{5i-i^2}{i^2}$$

Now, using the fact that $i^2=-1$, we have:

$$c=\frac{5-i}{i}\cdot\frac{i}{i}=\frac{5i-i^2}{i^2}=\frac{5i-(-1)}{-1}=\frac{5i+1}{-1}=-1-5i$$ :D