Simplify the expression. -5+i/2i
1/2+5/2i right?
Just multiply top and bottom by i.
What do you get, since i^2 = -1 ?
correct
although the way you wrote it could easily be seen as 1/2 + 5/(2i), especially since that is the way you meant it in your original expression.
Since you know what you meant, and you're probably submitting it in writing, it will probably come out ok, but online you need to make it clear. Try
1/2 + 5/2 i
or
1/2 + (5/2)i
To simplify the expression (-5 + i) / (2i), we can follow these steps:
Step 1: Distribute the denominator:
(1 / 2i) * (-5 + i)
Step 2: Simplify the denominator:
To simplify the denominator, we need to rationalize it. Multiply the numerator and denominator by the conjugate of 2i, which is -2i:
((-5 + i) * -2i) / ((2i) * (-2i))
(-5 * -2i + i * -2i) / (4i^2)
Step 3: Simplify the numerator:
(-5i + 2i^2) / (4i^2)
Step 4: Simplify the powers of i:
Since i^2 is equal to -1, the expression becomes:
(-5i + 2 * -1) / (4 * -1)
Step 5: Simplify the numerator and denominator independently:
(-5i - 2) / -4
Step 6: Divide each term by -4:
-5i / -4 - 2 / -4
Step 7: Simplify the fractions:
5i / 4 + 1/2
So, the simplified expression is:
5i / 4 + 1/2