let z=-3+2i. find r and Q. draw the angle Q and leave your answer in polar form
To find the magnitude (r) and argument (θ) of z, we can use the formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Given that z = -3 + 2i, we can see that x = -3 and y = 2.
Using these values, we can calculate r and θ:
r = √((-3)^2 + 2^2)
= √(9 + 4)
= √(13)
θ = arctan(2/-3)
= atan(-2/3) (approx. -0.588 radians or -33.69 degrees)
Therefore, in polar form, z can be written as:
z = √(13) * e^(-0.588i)