A and C are points in the Argand diagram representing the complex numbers 1 + i and 7 + 3i respectively. Given that AC is a diagonal of the square ABCD, calculate the complex numbers represented by the points B and D. Thanks.
all complex numbers are written as "z=x+iy" where 'i' = sqrt( -1). Since sqrt(-1) can't be mixed with real numbers, we sort it into the "real" and "imaginary". x is the real part, and can be plotted on a number line, but iy can't and is therefore separated. So, instead of using the Cartesian plane where both axis's represent "real" numbers, we make a new one where the y axis is the "imaginary" part (hence iy), and the x axis is the "real" numbers. For example, 2+3x(sqrt(-1)) is in its simplest form as they can not mix. It would fall onto the complex plane (the new graph) at the co-ordinates (2,3) as the real part is worth 2, and the imaginary part is worth 3. I hoped this helped but it is kinda dodgy as it is hard to explain over text.
Bombelli and Cardano solves cubic equations that had no ‘real’ solution by defining square root of -1 as i, and I guess it kinda stuck. It doesn’t come from the word imaginary
@@missghani8646 The term "imaginary" was coined by Renee Descartes, who was a critic of the concept of imaginary numbers, and somehow that name managed to stand the test of time for what we call them today. A similar example of a term coined by a critic, rather than a proponent, is "big bang" as the name for the origin of the universe. The letter i is therefore the choice for what we call the imaginary unit of sqrt(-1). In engineering, it is called j, because i is spoken-for to stand for current. Gauss had suggested calling them lateral numbers instead of imaginary numbers, which is an idea I agree with, since that is more descriptive of what they are. Had Gauss's suggestion stuck, we'd be calling it ℓ. Maybe we could call them Italian Numbers, and still keep the name i.
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you are SUCH a good teacher !
he kicks ass
definitely need to make these longer, so interesting!
Your the best teacher that i evered seen in my life
Amazing explanation
All things aside i love his tie.
Your explanation of the notation is very valuable to me. Here’s a math problem for you. How come given a 50/50, chance I get it wrong 100% every time?
You haven't tried enough times.
A and C are points in the Argand diagram representing the complex numbers 1 + i and 7 + 3i respectively. Given that AC is a diagonal of the square ABCD, calculate the complex numbers represented by the points B and D. Thanks.
Is this for maths degree
A level
It’s, a course in the Australian schooling. For year 12’s like 17-18 year old
It's in the course of 11th standard in India
@@studyplusmathematics562 12th in some boards like for me
@@alexsanders7303 im aussie and im doing this right now in year 10
Hyberbolic functions and the hyperboloid in anti-de-sitter space and the holographic principle haha.
can someone please say from where the (i) in "z=x+iy" came?
all complex numbers are written as "z=x+iy" where 'i' = sqrt( -1). Since sqrt(-1) can't be mixed with real numbers, we sort it into the "real" and "imaginary". x is the real part, and can be plotted on a number line, but iy can't and is therefore separated. So, instead of using the Cartesian plane where both axis's represent "real" numbers, we make a new one where the y axis is the "imaginary" part (hence iy), and the x axis is the "real" numbers. For example, 2+3x(sqrt(-1)) is in its simplest form as they can not mix. It would fall onto the complex plane (the new graph) at the co-ordinates (2,3) as the real part is worth 2, and the imaginary part is worth 3. I hoped this helped but it is kinda dodgy as it is hard to explain over text.
it does make sense, thank you so much
Bombelli and Cardano solves cubic equations that had no ‘real’ solution by defining square root of -1 as i, and I guess it kinda stuck. It doesn’t come from the word imaginary
In short, it is represented in cartesian form.
@@missghani8646 The term "imaginary" was coined by Renee Descartes, who was a critic of the concept of imaginary numbers, and somehow that name managed to stand the test of time for what we call them today. A similar example of a term coined by a critic, rather than a proponent, is "big bang" as the name for the origin of the universe.
The letter i is therefore the choice for what we call the imaginary unit of sqrt(-1). In engineering, it is called j, because i is spoken-for to stand for current.
Gauss had suggested calling them lateral numbers instead of imaginary numbers, which is an idea I agree with, since that is more descriptive of what they are. Had Gauss's suggestion stuck, we'd be calling it ℓ. Maybe we could call them Italian Numbers, and still keep the name i.
second