Answer:
The correct statements describing the process of converting z = 2 + 3i to polar coordinates using technology are:
Write the complex number as a point in the complex plane: (2, 3i)
Substitute a = 2 and b = 3 for the real and imaginary parts respectively.
Using radians for θ, record the result as r = 3.606 and θ = 0.983 as your answer in polar coordinate form: (3.606, 0.983).
To convert a complex number in the form of z = a + bi to polar coordinates using technology, we can use the following steps:
Write the complex number as a point in the complex plane, with the real part as the x-coordinate and the imaginary part as the y-coordinate.
Substitute a for the real part and b for the imaginary part.
Using the Pythagorean theorem, we can find the distance from the origin to the point, which is the magnitude or modulus of the complex number, represented by r.
Using the tangent function, we can find the angle of the point from the positive x-axis, which is the argument or phase of the complex number, represented by θ.
Record the result in polar coordinates as (r, θ), where r is the magnitude and θ is the argument, given in radians.
It's also worth noting that polar coordinates can also be represented in the form of (r, θ ) or (r, arg(z)) or (r, angle(z))