Let Z=-3+2i
Find r and Q.
Draw the angle Q and leave your answer in polar form
To find the magnitude, r, of the complex number, we use the formula:
|r| = √(a^2 + b^2)
Where a is the real part (-3) and b is the imaginary part (2).
|r| = √((-3)^2 + 2^2)
|r| = √(9 + 4)
|r| = √13
Therefore, r = √13.
To find the argument, Q, of the complex number, we use the formula:
Q = arctan(b/a)
Where a is the real part (-3) and b is the imaginary part (2).
Q = arctan(2/(-3))
Q = arctan(-2/3)
Using a calculator, we find Q ≈ -33.69°.
Therefore, in polar form, Z = √13 * cis(-33.69°)