Simplify the expression.
-5+i/2i
Please show how you get there and explain it. I'm struggling with this one.
(-5+i) / 2i * -2i/-2i = -2i(-5+i)/4 = 1/2 + 5/2 i
Sorry I meant (-5+i)/2i
To simplify the expression (-5 + i) / (2i), we can use the technique of rationalizing the denominator. Rationalizing the denominator means eliminating any imaginary unit (i) from the denominator by multiplying both the numerator and denominator by its conjugate.
The conjugate of 2i is -2i since a conjugate is obtained by changing the sign of the imaginary part. By multiplying the numerator and denominator by -2i, we can eliminate the imaginary unit in the denominator:
((-5 + i) / (2i)) * (-2i / -2i)
Working through the expression, we have:
((-5 + i) * (-2i)) / (2i * -2i)
(10i - 2i^2) / (-4i^2)
Simplifying further, we can recall that i^2 equals -1:
(10i - 2 * -1) / (-4 * -1)
(10i + 2) / 4
Now we can split the expression into two parts, the real part and the imaginary part:
10i / 4 + 2 / 4
Simplifying the real part, divide the numerator by the denominator:
10i / 4 = 5/2 * i
And simplifying the fraction in the imaginary part:
2 / 4 = 1/2
Therefore, the simplified expression is:
(5/2)i + 1/2