Let z =-3+2i, find r and q. Draw the angle q and leave the answer in polar form
To find r and q, we can use the formula for polar form:
r = √(Re(z)^2 + Im(z)^2)
q = atan(Im(z)/Re(z))
Given z = -3 + 2i, we can see that Re(z) = -3 and Im(z) = 2. Plugging these values into the formulas, we have:
r = √((-3)^2 + 2^2)
= √(9 + 4)
= √13
q = atan(2/(-3))
Using the inverse tangent function, we find that q is the angle whose tangent is 2/(-3) in the fourth quadrant. Therefore, q = -56.31 degrees.
In polar form, z is represented as z = r(cos(q) + i*sin(q)).
Plugging in our values of r and q, we have:
z = √13(cos(-56.31) + i*sin(-56.31))
This is the answer in polar form.