Question

The problem is (-5+i)/2iI would like a clear explanation on the process of doing it. I am having trouble understanding the concept, so a very clear explanation would be helpful.

Answer 1

In order to simplify the expression, let's divide each term in the numerator by the denominator:

`(-5+i)/(2i)=(-5)/(2i)+(i)/(2i)=-(5)/(2i)+(1)/(2)`

Then, to remove the complex number i from the denominator of the first fraction, let's multiply the numerator and denominator by i:

`-(5)/(2i)+(1)/(2)=-(5\cdot i)/(2i\cdot i)+(1)/(2)=(-5i)/(2i^2)+(1)/(2)=(-5i)/(2\cdot(-1))+(1)/(2)=(-5i)/(-2)+(1)/(2)=(5)/(2)i+(1)/(2)`

Therefore the complex number in the form a + bi is equal to 1/2 + (5/2)i.