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Rectangular coordinates (sqrt3,sqrt3) and polar coordinates (r,0) = (sqrt6, pi/4) both represent the same complex number z.
Which set of equations demonstrates why both sets of coordinates represent the same number?

Respuesta :

abidemiokin

The equation that demonstrates why both sets of coordinates represent the same number is z = √3(cosπ/4 + isinπ/4)

Rectangular coordinates

The transformation of rectangular to polar coordinates is expressed as:

(x, y) -> (r, Ф)

where;

  • x = r cos Ф
  • y = r sin Ф

Given the complex number z = x + iy

|z| = √x² + y²

|z| =√(√3)²+ (√3)²
|z| = √6

To get the argument;

Ф = arctan(√3/√3)

Ф = arctan(1)

Ф = 45 degrees = π/4

The resulting equation that represeent the complex number will be:

z = r(cosФ + isinФ)

z = √3(cosπ/4 + isinπ/4)

Hence the equation that demonstrates why both sets of coordinates represent the same number is z = √3(cosπ/4 + isinπ/4)

Learn more on transformation here: https://brainly.com/question/2644832

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