Question

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
+
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Answer 1

well, let me put it this way.

`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}{√(3)}~~,~~\stackrel{y}{√(3)})\qquad \qquad \begin{array}{llll} \stackrel{\textit{is assuming that}}{r^2=(√(3))^2+(√(3))^2}\implies r=\sqrt{(√(3))^2+(√(3))^2}\\\\ \stackrel{\textit{is also assuming that}}{\theta =tan^(-1)\left( \cfrac{√(3)}{√(3)} \right)}\implies \theta =tan^(-1)(1)\implies \theta =\cfrac{\pi }{4} \end{array}`