Remember when you were in grammar school, and you were first learning about the square root, and how they told you that you couldn’t take the square root of a negative number? They lied.

OK, they didn’t exactly lie to you, though what they should have told you was “for now, you can’t take the square root of a negative number.” Eventually, though, you would have to come to grips with the fact that, sometimes, it was necessary to pretend that you could, like when you were faced with the equation

a^{2} + 4 = 0

In this case, you know that a^{2} = -4, so a = √-4. Now, understand, you still can’t take the square root of a negative number, but we can always imagine that we can. Now, √-4 = √-1 · √4. The square root of 4 is 2, and let’s call the square root of -1 i, the i standing for “imaginary.” (Saying that the i stands for “imaginary” might make a few mathematicians scowl, but screw ’em if they can’t take a joke.)

Numbers of the form a + bi, where a and b are real numbers, are called complex numbers, because they’re made up of a real part and an imaginary part. You can even plot them on graph paper, with the real part on the x axis and the imaginary part on the y axis. That makes your graph an Argand diagram.

That’s all I want to say about complex numbers, other than to say that they make it possible to solve some equations in science and engineering. Just take my word for it…

Ouch, math… I have somewhat of a difficult relationship with it. I love it, but my brain isn’t so enamored with it to study it deeper. The only bit I always succeeded at at school was geometry.

Geometry totally baffled me. It might have just been a difficult time (new school and all) or because I didn’t study hard enough (most likely) or that I’d think I’d know what I was doing and then stop myself. When I started at the new school they wanted to put me in a lower level for geometry and I talked them out of it. I think it was a matter of pride. What can I say? I was 15…

In Poland teaching is different, so you have to achieve certain levels of all the math areas to advance to the next year, so I guess I was kind of “eased” into it. And it was more appealing than, let’s say, trigonometry, as it always had real-life applications. π

Imaginary numbers are not useful to most people, but once electricity changed from DC to AC, they are valuable for every electrical engineer in order to calculate AC current and voltage.

Funny! My daughter just finished a course that included imaginary numbers! And the square root of negatives too. I will be sending her the link for this post.

In the play “Love and Information”, there’s a scene entitled “Imaginary Numbers”. It contained one of my favorite lines: “Can you have an imaginary number of oranges?” That pretty much sums up my view of complex math. π

I’ll take your word for it! I wish I could understand complex mathematics, since people who have a calling for it say there’s great beauty and art in those equations and numbers.

Sitting in my apartment complex thinking about how complex this math situation is. Perplexed (you can use that one for P if you haven’t already assigned it!)

Oh my! Where have you been when I was in high school? Thanks for the school memories, I can’t believe I was actually good at algebra. Now as I see my kids talking about math problems I hide under the dining table.

Yipes, I left all that mess back in college. I really liked math, but nobody ever showed me any practical application for it, so it held no meaning to me… I did ace statistics at the university which astounds me to this day!

OMG Mr. John, youβre a genius!! You and my husband and oldest son are totally on the same page when it comes to the mathematical stuff. My son when he was in 3rd grade, yes 3rd grade was trying to explain the Pythagorean theory to me. Still donβt get it and donβt even try. He got a perfect score on the math ACTββs and SATβs.. Iβm hoping I just explained it right. How cool π aye you a writer and a genius mathematician. W O W

Well I may have you beat on the ephemera π now if I could just pronounce it grammatically. Itβs just one of those words I have to think about before I say it!! Happy Thursday, Mr. John. Love your blog, I always learn something new when I read it !!!

I will take your word for it! I used to love solving word problems and equations, but those days are long gone…

Beth

http://bethlapinsatozblog.wordpress.com/

LikeLike

I understood it well enough ton get through Differential Equations, but that was about it.

LikeLiked by 1 person

I’m impressed – always impressed with the things you come up with for your posts!

LikeLike

I have no idea how I come up with this stuff, but I’m glad you enjot it.

LikeLiked by 1 person

You’re just that amazing, that’s all! Keep running with it!! π

LikeLike

Ouch, math… I have somewhat of a difficult relationship with it. I love it, but my brain isn’t so enamored with it to study it deeper. The only bit I always succeeded at at school was geometry.

LikeLike

Geometry totally baffled me. It might have just been a difficult time (new school and all) or because I didn’t study hard enough (most likely) or that I’d think I’d know what I was doing and then stop myself. When I started at the new school they wanted to put me in a lower level for geometry and I talked them out of it. I think it was a matter of pride. What can I say? I was 15…

LikeLiked by 1 person

In Poland teaching is different, so you have to achieve certain levels of all the math areas to advance to the next year, so I guess I was kind of “eased” into it. And it was more appealing than, let’s say, trigonometry, as it always had real-life applications. π

LikeLike

That is complex because my eyes went cross-eyed:)

LikeLiked by 1 person

Many people feel the same way.

LikeLike

Imaginary numbers are not useful to most people, but once electricity changed from DC to AC, they are valuable for every electrical engineer in order to calculate AC current and voltage.

LikeLike

Exactly. They’re useful if you’re an engineer, which I wasn’t…

LikeLike

Yikes John, but thank you. I like numbers muchly but this is seriously complex ..

LikeLike

It’s much harder than it looks.

LikeLike

Math lesson for the day! Thanks! π

LikeLike

You’re welcome!

LikeLiked by 1 person

π

LikeLike

I thought I was listening to my father. As Beth said (above), I’ll take your word for it.

LikeLike

I ended where I did because I was getting into areas where the discussion could become a little too complex…

LikeLike

It’s comforting to see someone else venture into math in a blog post, John. May you have better luck than I have had.

LikeLike

I take the occasional

sortieinto math here once in a while, though I tend to keep it to things that I actually understand…LikeLiked by 2 people

Funny! My daughter just finished a course that included imaginary numbers! And the square root of negatives too. I will be sending her the link for this post.

LikeLike

In the play “Love and Information”, there’s a scene entitled “Imaginary Numbers”. It contained one of my favorite lines: “Can you have an imaginary number of oranges?” That pretty much sums up my view of complex math. π

LikeLike

Definitely will take your word for it, John. I got a headache looking at those equations. More power to the people who actually know what they mean.

LikeLike

Too complex.

LikeLike

I have to deal with maths for every quilt I make, but try to keep them simple ;))

Quilting Patchwork & AppliquΓ©

LikeLike

I’ll take your word for it – because now I’m utterly confused. I think I’ll stick to playing with words LOL

LikeLike

I’m math challenged so I’m out of my depth here. But I have to say I delight in a world where there are both complex numbers and imaginary ones.

LikeLike

I’ll take your word for it! I wish I could understand complex mathematics, since people who have a calling for it say there’s great beauty and art in those equations and numbers.

LikeLike

You can’t but you can. It is but it isn’t. Poetry works that way, too.

LikeLike

Sitting in my apartment complex thinking about how complex this math situation is. Perplexed (you can use that one for P if you haven’t already assigned it!)

LikeLike

Iβll take your word for it. Imaginary numbers … who knew? Guess I blocked that from my memory banks.

LikeLike

Oh my! Where have you been when I was in high school? Thanks for the school memories, I can’t believe I was actually good at algebra. Now as I see my kids talking about math problems I hide under the dining table.

LikeLike

Yipes, I left all that mess back in college. I really liked math, but nobody ever showed me any practical application for it, so it held no meaning to me… I did ace statistics at the university which astounds me to this day!

LikeLike

Math was never my thing, but I’m taking your word for it!

https://seal-of-melchizedek.blogspot.com/2019/04/dallas-texas-temple.html

LikeLike

Probably best that way…

LikeLike

Heh, my head started to hurt about half way through your post…

LikeLike

Mine was hurting when I got to the last paragraph and I decided that I’d have too much to re-learn to continue.

LikeLike

OMG Mr. John, youβre a genius!! You and my husband and oldest son are totally on the same page when it comes to the mathematical stuff. My son when he was in 3rd grade, yes 3rd grade was trying to explain the Pythagorean theory to me. Still donβt get it and donβt even try. He got a perfect score on the math ACTββs and SATβs.. Iβm hoping I just explained it right. How cool π aye you a writer and a genius mathematician. W O W

LikeLike

I’m not so much a genius in math as a collector of ephemera, I think. When I hit real analysis and abstract algebra, my mind shut down…

LikeLiked by 1 person

Well I may have you beat on the ephemera π now if I could just pronounce it grammatically. Itβs just one of those words I have to think about before I say it!! Happy Thursday, Mr. John. Love your blog, I always learn something new when I read it !!!

LikeLike

Gross. I couldn’t read this. It was worse than baseball!

You really do write well, I tried, lol! Math and I just don’t meet beyond basic computation!

LikeLike