Simplifying the expression
(-5+i)/(2i)
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.
To simplify the expression (-5+i)/(2i), we can multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of 2i is -2i, so we can multiply the numerator and denominator by -2i:
((-5+i)/(2i)) * (-2i/-2i)
Multiplying the numerator and denominator gives us:
(-5i - i^2) / (-4i^2)
Simplifying further:
(-5i - i^2) / (-4(-1))
Since i^2 is equal to -1:
(-5i - (-1)) / 4
(-5i + 1) / 4
So the simplified expression is (-5i + 1) / 4.
To simplify the expression (-5+i)/(2i), we need to first multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of 2i is -2i. Multiplying the numerator and denominator by -2i gives us:
((-5+i)/(2i)) * ((-2i)/(-2i))
= (-5 * -2i + i * -2i) / (2i * -2i)
= (10i - 2i^2) / (-4 * i^2)
Now, recall that i^2 is defined as -1. Substituting this value into the expression gives us:
(10i - 2(-1)) / (-4 * (-1))
= (10i + 2) / 4
Simplifying further, we can divide both the numerator and denominator by 2:
(10i + 2) / 4
= 10i/4 + 2/4
= (5/2)i + (1/2)
Therefore, the simplified expression for (-5+i)/(2i) is (5/2)i + (1/2).
this is wrong ðŸ˜
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).