This is actually a very good way to explain also the 4-repetition of taking i to different exponents rather than just taking it for granted that it's how it works.
raymondx
I found this slide very eye opening. I have learned about complex numbers before but was never taught to think in the manner that i/j is just a CCW rotation around the complex plane.
bpopeck
I really like this geometric interpretation which was sadly absent from how complex numbers were taught in my high school. I remember coming across this article which gives the geometric interpretation and also compares the non-intuitive nature of i^2 = -1 to how negative numbers were received by mathematicians when they were introduced into systems of arithmetic.
This timeline shows how some famous mathematicians rejected or struggled for a time with the idea of a negative number. I think this shows that it is a reasonable first reaction to reject complex numbers when presented with the identity i^2 = -1, but looking at the geometric interpretation can convince you that complex numbers are a useful abstraction :)
Osoii
I really wish I could know this geometric description earlier :(
I did a project in undergrad, and I dealt a lot with quaternions, the complex numbers just confused me a lot, and now things become much clearer.
This is actually a very good way to explain also the 4-repetition of taking i to different exponents rather than just taking it for granted that it's how it works.
I found this slide very eye opening. I have learned about complex numbers before but was never taught to think in the manner that i/j is just a CCW rotation around the complex plane.
I really like this geometric interpretation which was sadly absent from how complex numbers were taught in my high school. I remember coming across this article which gives the geometric interpretation and also compares the non-intuitive nature of i^2 = -1 to how negative numbers were received by mathematicians when they were introduced into systems of arithmetic.
This timeline shows how some famous mathematicians rejected or struggled for a time with the idea of a negative number. I think this shows that it is a reasonable first reaction to reject complex numbers when presented with the identity i^2 = -1, but looking at the geometric interpretation can convince you that complex numbers are a useful abstraction :)
I really wish I could know this geometric description earlier :( I did a project in undergrad, and I dealt a lot with quaternions, the complex numbers just confused me a lot, and now things become much clearer.