Question

if you were asked to convert the complex number, -6 + 8i, into polar form, what values of “r” and “0” would be in polar form?

Answer 1

10∠126.87°

r = 10; θ = 126.87°

Explanation:

The coordinate conversion from (x, y) or (x +yi) to (r; θ) can be done using the relations ...

r = √(x² +y²)

θ = arctan(y/x) . . . . paying attention to quadrant

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For the given complex number, we have ...

r = √((-6)² +8²) = √(36 +64) = √100 = 10

θ = arctan(8/(-6)) = arctan(-4/3) . . . . in the 2nd quadrant

θ ≈ -53.13° +180° = 126.87°

The equivalence is ...

-6 +8i ⇔ 10∠126.87° . . . . . in the form r∠θ

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Additional comment

Many scientific and graphing calculators are equipped to work with complex numbers, including their conversion to or from polar form.