The rectangular coordinates (√3,√3) and polar coordinates (√6,[tex]\frac{\pi}{4}[/tex]) represent the same complex number z=x+iy because,
[tex]r=\sqrt{(\sqrt3)^2+(\sqrt3)^2}=\sqrt6[/tex] and,
[tex]\theta=\arctan(\frac{\sqrt3}{\sqrt3})=\arctan(1)=\frac{\pi}{4}[/tex]
The question is not written in an understandable manner look at the question in the below-given image.
What is polar coordinate?
In terms of Cartesian coordinates, the polar coordinates r (the radial coordinate) and θ (the angular coordinate, often known as the polar angle),
x = rcosθ
(1)
y = rsinθ,
(2)
where r is the radial distance from the origin and θ is the counterclockwise angle from the x-axis. In relation to x and y,
[tex]r=\sqrt{x^2+y^2}[/tex]
(3)
[tex]\theta=\arctan(\frac{y}{x})[/tex]
How to solve it?
Using the above explanation of polar coordinates we have that
[tex]r=\sqrt{(\sqrt3)^2+(\sqrt3)^2}=\sqrt6[/tex] and
[tex]\theta=\arctan(\frac{\sqrt3}{\sqrt3})=\arctan(1)=\frac{\pi}{4}[/tex]
Learn more about polar coordinates here-
brainly.com/question/18068617
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