Convert (-2,3) to polar form written in 2 different forms?

Answer 1

To convert from cartesian to polar coordinates, the formulas are:

r = √(x² + y²)
θ = arctan(y/x)

so r = √((-2)² + (3)²) = √(4 + 9) = √13

and θ = arctan(y/x) = arctan(3/-2) = -56.3°

But you can also add or subtract 360° as many times to theta as you want and you still get the same angle.

So two possible representations would be:

(√13, -56.3°) and
(√13, 303.7°)

Answer 2

first the bijection of (-2,3) in the complex plan is -2+3i
that gives modulus is root( 2^2+3^2)=root(13)
and the argument =arctan(-3/2)

Answer 3

y = x => r sin(theta) = r cos(theta) Cancel r, sin(theta) = cos(theta) => tan(theta) = one million => theta = pi/4 or 40 5 tiers for the reason that r is canceled, r could be any fee. subsequently, in polar coordinate, theta = pi/4 represents a rapidly line which has an perspective of pi/4 with the useful process x-axis.