Question

The polar coordinates

and (0,6) both represent the complex number 6i.
A) True
B) False

Answer 1

Answer: true

Explanation:

The polar cordinates are (6, pi/2)

We know that a imaginary number can be written, in polar cordinates (R, θ)

Z = R*(cos(θ) + i*sin(θ))

Then, the point (6, pi/2) is:

Z = 6*(cos(pi/2) + i*sin(pi/2)) = 6i

The other representation is (a, b) and in this case the imaginary number is

Z = a + b*i

In this case we have (0, 6) so:

Z = 0 + 6*i

Then you can see that the statement is true,