Question

In the complex plane, the rectangular coordinates (x, y) represent a complex number. Which statement explains why polar coordinates (r, θ) represent the same complex number?

Answer 1

its b

Explanation:

trust

Answer 2

Answer: second option (counting from the top)

Explanation:

When we have a number:

z = x + y*i

we can represent this with the point:

(x, y).

Now, remember that in polar coordinates, we need to use the variables:

r = distance to the (0, 0), or the "magnitude" of the point.

θ = angle measured counterclockwise from the x-axis.

r is easy to find, is the magnitude, this is calculated as:

r = √(x^2 + y^2)

To find θ, suppose that we have a triangle rectangle, where x is the adjacent cathetus, and y is the opposite cathetus, and θ is the angle as we described it.

We know that:

Tan(θ) = opposite cathetus/adjacent cathetus = y/x

Tan(θ) = y/x

Then:

θ = Tan^-1 (y/x)

Then the correct option is the second option (counting from the top)