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Tag: e
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Forms of Complex Numbers In the previous post, The Tripartite Fugue, we finally obtained the exponential form for complex numbers. As mentioned in the previous post, we will conclude our series on complex numbers today. Here I wish to explore a couple of aspects of complex numbers that become evident from the exponential form. I…
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Milestones on the Journey After a three week break, most of which was spent grading IB papers, I am back. We continue with our series on complex numbers. By the time we last dealt with this, in Deriving Derivatives – Part 2, we had obtained the derivatives for a few functions as follows: In the post…
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Signing In In the previous post, Deriving Derivatives – Part 1, which is part of the second pit stop in our exploration of complex numbers, we had derived the derivatives of xn and sin x. I had informed you that we will derive the derivatives of the exponential and logarithmic functions. In case some of you…
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Resumption Last week I had taken a break for Good Friday. For those who are interested, I used a random event for my sermon. If you’re interested, you can find it here. Anyway, with the break behind us, we resume the series on complex numbers. In the previous post of the series, Pole Vaunting, we…
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In the last three posts, we have been dealing with some issues related to counting. In Learning to Count, I introduced us to the area of combinatorics and specifically combinatorial arguments. In the second post, Abjuring Double Counting, we looked at the inclusion-exclusion principle that is used to ensure that every element is counted exactly…
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Recapitulation We have reached our final post in this series on the number e. In the first post of the series, we introduced e and looked at the reasons for which it is the base of the natural logarithm and the exponential function. In the second post of the series, we used various techniques to…
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Recapitulation I’m back with another post after taking a break for a week. The last week of May was particularly busy as I was teaching a class called Introduction to the New Testament. During the week I also gave a lecture on Causes and Symptoms of Religious Discord, which you can find here if you’re…
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Recap In the previous post, I started a series of three posts focused on the number denoted by e. We then saw why it is the base of the natural logarithm and the base of the exponential function. We also saw the relation between e and compound interest. In this post we will try to…
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In the opening post of this blog, I had introduced Euler’s Identity, which states The identity combines five numbers – 0, 1, e, i, and π – and three mathematical operators – addition, multiplication, and exponentiations – and the equality. In other words, this identity captures many diverse parts of mathematics and links them, thereby…
Acutely Obtuse 