Question

Simplifying the expression

(-5+i)/(2i)

Answer 1

To simplify the expression (-5+i)/(2i), we can multiply both the numerator and the denominator by the conjugate of 2i, which is -2i. This will eliminate the complex number in the denominator.

(-5+i)/(2i) * (-2i)/(-2i)

Simplifying the numerator and the denominator:

(-5+i)(-2i) / (2i)(-2i)

Using the FOIL method to multiply the numerator:

(-5)(-2i) + (i)(-2i) / (2i)(-2i)

Simplifying:

10i + 2i^2 / -4i^2

Since i^2 is equal to -1, we can simplify further:

10i + 2(-1) / -4(-1)

Update the i^2 and perform the multiplication:

10i - 2 / 4

Simplify further by dividing 2 by 4:

10i - 1/2

So, the simplified expression is 10i - 1/2.

Answer 2

this is wrong 😭

Answer 3

Apologies for the mistake. Let's re-evaluate the expression.

To simplify the expression (-5+i)/(2i), we can multiply the numerator and denominator by -i to eliminate the complex number in the denominator.

((-5+i)/(2i)) * (-i/-i)

Simplifying the numerator and denominator:

(5i - i^2) / (2i * -i)

Since i^2 is equal to -1, we can simplify further:

(5i - (-1)) / (-2i)

Simplify the subtraction in the numerator:

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

Now, we can divide both the numerator and denominator by -1:

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

Finally, we can distribute the negative sign:

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

Therefore, the simplified expression is (-5i - 1) / (2i).