Mathematics, 13.02.2022 18:30 jennmcd17
Rectangular coordinates (73,73) and polar coordinates (6,0) = (V6,4) both represent the same complex number z.
Which set of equations demonstrates why both sets of coordinates represent the same number?
Or=v3 + V3 = V6 and 8 = tan-|(1) =
품
Or=V3 + V3 = V6 and 8 = tan-(3)
4
Or=763)2 + (13)2 = V and a = tan-f(1) = = I
TT
O r=(73)+ (73)2 = 76 and 8 = tan-(73) = 1
+
-
Answers: 2
![r^2=x^2+y^2\qquad \qquad \qquad \theta =tan^{-1}\left( \cfrac{y}{x} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{\sqrt{3}}~~,~~\stackrel{y}{\sqrt{3}})\qquad \qquad \begin{array}{llll} \stackrel{\textit{is assuming that}}{r^2=(\sqrt{3})^2+(\sqrt{3})^2}\implies r=\sqrt{(\sqrt{3})^2+(\sqrt{3})^2}\\\\ \stackrel{\textit{is also assuming that}}{\theta =tan^{-1}\left( \cfrac{\sqrt{3}}{\sqrt{3}} \right)}\implies \theta =tan^{-1}(1)\implies \theta =\cfrac{\pi }{4} \end{array}](/tpl/images/2658/1123/ae3c9.png)
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Rectangular coordinates (73,73) and polar coordinates (6,0) = (V6,4) both represent the same complex...
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