Simplify the expression
-5+i/2i
-5+i over 2i
i-5/2i
what i see nah
(-5+i)/2i = -5/(2i) + 1/2
Now, 1/i = -i, since i^2 = -1
Thus we end up with
1/2 + 5/2 i
or (1+5i)/2
just learn something god bless u sir
It all comes with experience. You might just note that the powers of i cycle in periods of 4:
i^-4 = 1
i^-3 = 1/i^3 = 1/-i = i
i^-2 = 1/i^2 = -1
i^-1 = 1/i = -i
i^0 = 1
i^1 = i
i^1 = -1
i^3 = -i
i^4 = 1
...
To simplify the expression (-5 + i) / (2i), we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of 2i is -2i. Therefore, we can rewrite the expression as:
((-5 + i) / (2i)) * ((-2i) / (-2i))
Now, let's simplify each part of the expression:
Numerator: (-5 + i) * (-2i) = 10i - 2i^2 = 10i + 2 (since i^2 = -1)
Denominator: 2i * (-2i) = -4i^2 = -4*(-1) = 4
Now, we can rewrite the expression as:
(10i + 2) / 4
To simplify further, we can divide both the numerator and denominator by 2:
(10i + 2) / 4 = 10i/4 + 2/4
Simplifying the fractions:
10i/4 = (10/4)i = (5/2)i
2/4 = 1/2
Therefore, the simplified form of (-5 + i) / (2i) is:
(5/2)i + 1/2 or (5i + 1) / 2