The radius is the distance from (0, 0). It is found using the Pythagorean theorem.
r = √((-1)²+1²) = √2
The angle θ is found from the fact that r·sin(θ) = y = 1, and r·cos(θ) = x = -1. We take the ratio of these to get
... tan(θ) = 1/-1
... θ = arctan(-1) = 3π/4 . . . . . considering quadrant
Then the polar coordinates (r, θ) are (√2, 3π/4). You can multiply these by 1 = (-1, π) to get a negative value for r:
... (-1, 1) ⇒ (-√2, 7π/4)
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Multiplying numbers in polar coordinates multiplies their magnitudes and adds their angles.
