Question

Rewrite the equation in polar form.

Answer 1

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