Table of powers of complex numbers
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Table of powers of complex numbers by National Bureau of Standards.

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Written in English

Book details:

Edition Notes

 ID Numbers Statement by Herbert E. Salzer [for the National Bureau of Standards]. Series Applied mathematics series -- 8 Contributions Salzer, Herbert E. Open Library OL20215081M

To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis. See. Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts. See. Complex numbers can be multiplied and divided. In the powers of 4 table, the ones digits alternate: 4, 6, 4, 6. In fact, you can see that the powers of 4 are the same as the even powers of 2: 4 1 = 2 2 4 2 = 2 4 4 3 = 2 6 etc.   So, thinking of numbers in this light we can see that the real numbers are simply a subset of the complex numbers. The conjugate of the complex number $$a + bi$$ is the complex number $$a - bi$$. In other words, it is the original complex number . When you write your complex number as an e-power, your problem boils down to taking the Log of $(1+i)$. Now that is $\ln\sqrt{2}+ \frac{i\pi}{4}$ and here it comes: + all multiples of $2i\pi$. So in your e-power you get $(3+4i) \times (\ln\sqrt{2} + \frac{i\pi}{4} + k \cdot i \cdot 2\pi)$ I would keep the answer in e-power form.