Answer:
C) √5(cos(117°) +i·sin(117°))
Step-by-step explanation:
The rectangular number a+bi can be written in polar form as ...
√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))
Here, we have a=-1, b=2, so the magnitude is ...
√((-1)^2 +2^2) = √(1+4) = √5
and the angle is ...
arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle
Then you have ...
-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"
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Comment on the answer
The "polar form" is generally written as ...
(magnitude)·(cos(angle) +i·sin(angle))
You may also see it as ...
(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"
In my engineering courses, we often used the form ...
(magnitude) ∠ (angle)
The form used by my calculator is ...
(magnitude)·e^(i·angle) . . . . . where angle is usually in radians
