Simplify the expression -5+i/2i
I typed this problem into mathway and they told me the answer was 1/2+5i/2 but wouldn’t show me how they got it. They said to (“multiply by the conjugate and simplify”) but I have no clue on what the conjugate is and how to solve this problem. Can someone help explain better and show me how they came up with that answer please
For complex numbers,
a + bi and a - bi are called "conjugate' complex pairs
they have the interesting property that if you add them you get the real number 2a
and if you multiply them , because of the difference of square pattern, you get a^2 - b^2 i^2
But since i^2 = -1, we end up with a real number as a product.
e.g. 6 - 5i and 6 + 5i are conjugates of each other
sum = 6-5i + 6+5i = 12
product = 36 - 25i^2
= 36 -(-25) = 61
Your question is even easier, since the denominator is a monomial instead of a binomial, so we just have to multiply by i/i
Also I believe, according to the answer, that you have a typo, and you meant
(-5+i)/(2i)
= (-5+i)/(2i) *i/i
= (-5i + i^2)/2i^2)
= (-5i +i^2)/-2
= (-5i - 1)/-2
= (1 + 5i)/2 or they way they have it: 1/2 + 5i/2
@ who am I?, is your question 8 times 2.6? or 8x(2.6)? or 8x^2.6?
Well, let's solve this problem together and have some fun along the way!
We want to simplify the expression -5 + i / 2i.
First, let's multiply the numerator and denominator by the conjugate of 2i, which is -2i.
(-5 + i) * (-2i) / (2i * -2i)
Now, let's simplify the expression.
(-5 * -2i) + (i * -2i) / (4i^2)
This simplifies to:
10i - 2i^2 / 4 * (-1)
Since i^2 equals -1, we can substitute that in:
10i - 2 * (-1) / 4 * (-1)
Which becomes:
10i + 2 / 4
Now, let's simplify further:
10i / 4 + 2 / 4
Since 10i and 2 have a common denominator of 4, we can add them:
(10i + 2) / 4
So, the simplified expression is (10i + 2) / 4.
Voilà! We did it! Now you know how to simplify the expression -5 + i / 2i. Keep up the great work!
To simplify the expression (-5 + i) / (2i), we can use a technique called "rationalizing the denominator" by multiplying the numerator and denominator by the conjugate of the denominator.
The conjugate of 2i is -2i. We multiply the numerator and denominator by -2i:
((-5 + i) / (2i)) * (-2i / -2i)
Simplifying the numerator, we have (-5 + i) * (-2i), which can be expanded using the distributive property:
(-5 * -2i) + (i * -2i) = 10i - 2i^2
Since i^2 is equal to -1, we can substitute -1 for i^2:
10i - 2(-1) = 10i + 2
Now, let's simplify the denominator:
(2i) * (-2i) = -4i^2
Again, substituting -1 for i^2:
-4(-1) = 4
Putting it all together, we have:
(10i + 2) / 4
Now, we can simplify the expression by dividing both the numerator and denominator by 2:
(10i + 2) / 4 = 10i/4 + 2/4
This simplifies to:
(5i/2) + 1/2
Hence, the simplified expression is 5i/2 + 1/2, or written in a different order, 1/2 + 5i/2.
Therefore, the answer you received from Mathway, 1/2 + 5i/2, is correct.