Weekly Math Problem! #30

De Moivre's Theorem. Sometimes, when I'm thinking about what problem to post for the week, topics just come to mind. Somehow, DeMoivre and his theorem was this week's winner. 🎉 The last time I really encountered this topic was well over five years ago...way back when I took a precalculus course. Now that I think about it, 🤔 I don't recall going over this topic in any tutoring sessions over the years. But then again, I've been tutoring for a long time and may not really remember if I actually did or not. 🤷🏿

I would also like to say the following: When I learned this topic, I was enrolled in a summer school course--about four weeks long. I learned the topic quickly without knowing what the practical applications of the theorem is. It felt like the topic was being learned for the sake of learning it, without any real-world connections being made. Even though I didn't ask the question then, I can ask it now and find an answer somewhere on this internet. Okay, I am done with that small rant. 

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to convert complex numbers to polar form
        ✔️     How to apply DeMoivre's Theorem to find powers of complex numbers
        ✔️     How to evaluate trigonometric functions

WMP! #30 wants us to...

Happy solving!

Check back on Friday, December 4th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
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✏️📓 Solution Time! 📓✏️

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Lowkey, I was a little annoyed by the question, after I began solving it. 😒 I didn't realize the numbers were gonna be this crazy. 😅  As soon as I saw 520 ...👀...smh...no words. I realized it was too late to turn back now, so I pushed forward to finish. I will say this, I was getting nervous about whether or not I was correct and needed to verify my numbers. Oh the anxiety I was having. 

Before applying De Moivre's Theorem, some preliminary calculations need to be performed.

Notice, I rounded the angle, 𝛳, in degrees to the nearest thousandth. I didn't want use radians because I am more comfortable with degrees. Next up, the application of De Moivre's Theorem.

Do you see what I mean about the numbers being crazy? 🤪 ...in the trillions! I am aware that answer above is not as accurate as it should be, due to my rounding of 𝛳 to the nearest thousandth. So, I have prepared a more accurate calculation below. 

My final thought: I didn't find the problem difficult to execute. Anxiety was triggered in me when I saw the first large number in my calculation. The anxiety lead me to begin doubting my mathematical abilities. Even though I am good at math, I still very much understand, what it feels like to be fearful when doing it.

▪️ What kind of emotions do you feel when doing math??

▪️ Comment below with your responses and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next...WMP! #31

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Cheers!

The Younge Lady

Weekly Math Problem! #17

Complex Numbers. As if numbers weren't already complicated, there exist complex numbers. When did that happen and why? 🤷🏿😂🤦🏿‍♀️ I'm going a bit lite in this week's problem. (At least, I think it's lite.)

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  How to deal with imaginary numbers

    ✔️  How to multiply conjugates

    ✔️  How to square fractions

    

Here is WMP! #17...

Happy solving! 

Check back on Friday, August 28th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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Did you find the problem annoying? You can tell the truth. This is a no-judgment zone. Listen, a problem like this requires your attention because mistakes can easily be made. Did I find it annoying? Well, I didn't find it the opposite of annoying and that's my answer. 😁

I did the problem in two parts. The first part was just the squaring and simplification of the rational expression:

Once that was completed, I proceeded to the second part which consisted of rationalizing the denominator of the result:

I definitely did not get this on the first try. How did I know that I was incorrect on the first try? I used Mathway - Algebra to check my answer, because I know with all of those negative signs floating around, I could've easily made a mistake...and I did. So, I went back and searched my work to locate the error. These are the kind of problems a teacher would give as extra credit. 😅

◾️ How did you feel about squaring fractions and rationalizing the denominator?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Are we up to WMP! #18 already?

Cheers!

The Younge Lady