# Algebra

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

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1. 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

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2. can u guys help me u guys look like ur in college this is my question simplify 8x2.6 im confused im in middle school

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3. @ who am I?, is your question 8 times 2.6? or 8x(2.6)? or 8x^2.6?

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