Imaginary fraction questions. lost.

In summary, An imaginary fraction is a fraction where the numerator or denominator, or both, contain an imaginary number. To add or subtract imaginary fractions, you first need to find a common denominator. Then, you can simply add or subtract the numerators and keep the common denominator. You can simplify imaginary fractions just like regular fractions by dividing the numerator and denominator by their common factors. Multiplying imaginary fractions is similar to multiplying regular fractions, while dividing by an imaginary fraction requires multiplying by its reciprocal.
  • #1
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im studying for my circuits midterm and the proff has handouts with questions and answers but not detailed answers. i can't figure out how he went from a fraction to an answer.

(-j2)(2+j2)/-j2+2+j2 the answer on the paper is 2-j2


i do not know what I am allowed to do with the 2 next to the j with the distributive properties.


another example i was stuck on was i= -j2/1+j the answer here was rad2 at an angle of -135

and the above equation came from -j2+(2-j4) I_2 + (I_1 + I_2)j6=0 with I_1 =1

and insight or help would be appreciated. thakns
 
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  • #2
ahhgidaa said:
im studying for my circuits midterm and the proff has handouts with questions and answers but not detailed answers. i can't figure out how he went from a fraction to an answer.

(-j2)(2+j2)/-j2+2+j2 the answer on the paper is 2-j2
First off, you need to learn how to write mathematical expressions so that they mean what you intend. I am willing to bet that on the handout it looks like this:

[tex]\frac{-2j(2 + 2j)}{-2j + 2 + 2j}[/tex]

If you write fractions like this without using LaTeX to format them, put parentheses around the entire numerator and the entire denominator.

If you write 2j, people will be likely to mistake this for j2, which is something different.

For this problem, the first thing to do is to simplify the denominator.
ahhgidaa said:
i do not know what I am allowed to do with the 2 next to the j with the distributive properties.


another example i was stuck on was i= -j2/1+j
I'm guessing you mean i = -2j/(1 + j).

Look for an example where they rationalize the denominator by multiplying by the conjugate over itself.
ahhgidaa said:
the answer here was rad2 at an angle of -135

and the above equation came from -j2+(2-j4) I_2 + (I_1 + I_2)j6=0 with I_1 =1

and insight or help would be appreciated. thakns
 
  • #3
i ended up with -2j-j^2 which i^2 is -1 so i finally got the answer 2-2j and i copied it exactly how it was but ure way of putting it help me with the math. idk why he writes it like that
 
  • #4
1) Don't mix "j" and "i".

2) -2j- i^2= 1- 2j, not 2- 2j.

3) I think Mark44 meant to say that some would confuse "j2" with "j^2", not "2j".
 
  • #5
HallsofIvy said:
1) Don't mix "j" and "i".
The OP is in an electronics class - they write j for the imaginary unit, probably because i is used for electrical current. Still, the advice is good. Use one or the other consistently, but don't use both.
Mark44 said:
2) -2j- i^2= 1- 2j, not 2- 2j.

3) I think Mark44 meant to say that some would confuse "j2" with "j^2", not "2j".
Mark44 said:
Right, that's exactly what I meant.
 

1. What is an imaginary fraction?

An imaginary fraction is a fraction where the numerator or denominator, or both, contain an imaginary number. An imaginary number is any number that, when squared, results in a negative number.

2. How do you add and subtract imaginary fractions?

To add or subtract imaginary fractions, you first need to find a common denominator. Then, you can simply add or subtract the numerators and keep the common denominator. For example, to add 1/2i and 1/3i, we first find the common denominator, which is 6i. Then, we add the numerators to get 3/6i.

3. Can you simplify imaginary fractions?

Yes, you can simplify imaginary fractions just like regular fractions. If the numerator and denominator have a common factor, you can divide both by that factor to simplify the fraction. For example, if we have 2/4i, we can simplify it to 1/2i by dividing both the numerator and denominator by 2.

4. How do you multiply imaginary fractions?

Multiplying imaginary fractions is similar to multiplying regular fractions. You simply multiply the numerators and denominators separately and then simplify if needed. For example, to multiply 2/3i and 4/5i, we would get (2*4)/(3*5)i = 8/15i.

5. Can you divide by an imaginary fraction?

Yes, you can divide by an imaginary fraction, but you need to remember to multiply by its reciprocal instead. For example, to divide 2/3i by 4/5i, we would multiply by the reciprocal of 4/5i, which is 5i/4. This gives us (2/3i)*(5i/4) = 10i/12i^2 = 10i/(-12) = -5i/6.

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