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kondaur [170]
3 years ago
5

Show Work Find the slope (5,-3), (-7,0)

Mathematics
1 answer:
Alex777 [14]3 years ago
4 0
You'd use the equation y2-y1/x2-x1

0-(-3)/-7-5 = 3/-12 = -1/4

So -1/4 would be the slope
m= -1/4
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<img src="https://tex.z-dn.net/?f=z%5E%7B7%7D%3D128i" id="TexFormula1" title="z^{7}=128i" alt="z^{7}=128i" align="absmiddle" cla
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If <em>z</em> ⁷ = 128<em>i</em>, then there are 7 complex numbers <em>z</em> that satisfy this equation.

z^7 = 128i = 2^7i = 2^7e^{i\frac\pi2}

\implies z=\sqrt[7]{2^7} e^{i\frac17\left(\frac\pi2+2n\pi\right)}

(where <em>n</em> = 0, 1, 2, …, 6)

\implies z = 2 e^{i\left(\frac\pi{14}+\frac{2n\pi}7\right)}

\displaystyle\implies z = 2 \left(\cos\left(\frac\pi{14}+\frac{2n\pi}7\right)+i\sin\left(\frac\pi{14}+\frac{2n\pi}7\right)\right)

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