Question

Let z=-3+2i

Find r and q

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find r and q, we first need to express z in polar form.

The polar form of a complex number z = a + bi is given by z = r(cos(q) + isin(q)), where r is the magnitude (or absolute value) of z and q is the argument (or angle) of z.

First, we calculate the magnitude r of z:

r = sqrt((-3)^2 + 2^2) = sqrt(9 + 4) = sqrt(13)

Next, we calculate the argument q of z:

q = arctan(2/-3) = arctan(-2/3)

Therefore, the polar form of z is z = sqrt(13)(cos(arctan(-2/3)) + isin(arctan(-2/3))).

To determine r and q, we have:

r = sqrt(13)
q = arctan(-2/3)