Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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MathsIsFun
2005-12-04 07:51:31

I did a unit on electronics at uni. Failed the first test, but scraped through on final exam.

In that course, our prof said that the first person to use imaginary numbers in electonics was laughed at! His colleagues said "Imaginary? but circuits are Real ... hahahaha!"

So he used the maths to calculate a circuit which looked normal, but would in fact short-circuit. He then put the resistors and capacitors together, showed it to his colleagues, and said "Lo! A short-circuit!" They all laughed again.

So he said, "OK, attach a battery then!"

Phhzzztt!

They have used imaginary numbers ever since.

mathsyperson
2005-12-04 05:33:12

i and j are interchangeable.

Imaginary numbers can be helpful in engineering and engineers use j a lot because I would mean current, so using i would get confusing.

mikau
2005-12-04 05:11:28

j? My book always used i!

Btw, is there any practical use for imaginary numbers at all?

mathsyperson
2005-12-04 03:33:55

Putting a value like |this| means that you want the magnitude of it.

It doesn't matter what the direction is, it just wants how big it is.
Real and imaginary numbers are plotted at right-angles to each other, so you can use pythagoras.

|Z1| - |Z2| = |9+7j| - |8+3j| = √(9²+7²) - √(8²-3²)

= √130 - √73 ≈ 2.86

Ugly but true.

Lloyd
2005-12-04 03:20:13

Hi, i was stuck on a question and think i realised how to do it while i was writing it here. But im still not 100% sure i did it right. so....

Z1 = 9+7j
Z2 = 8+3j

find |Z1| - |Z2|