Question Info

This question is public and is used in 5 tests or worksheets.

Type: Multiple-Choice
Category: Complex Numbers
Level: Grade 11
Standards: HSN-CN.B.6
Author: nsharp1
Created: 5 years ago

View all questions by nsharp1.

Complex Numbers Question

View Find Similar

View this question.

Add this question to a group or test by clicking the appropriate button below.

Grade 11 Complex Numbers CCSS: HSN-CN.B.6

Kayslee is given the complex numbers C and J in polar form,

$2sqrt(5) \ (cos(63.4° + i sin63.4°)$ and

$sqrt(2) \ (cos(135° + isin135°)$ respectively. She notices that she can find the distance between these numbers,

$d$ , in the complex plane simply by taking the difference of their arguments,

$71.6°$ , and then applying the law of cosines formula,

$d = sqrt( (2sqrt(5))^2 + (sqrt(2))^2 - 2 * 2sqrt(5) * sqrt(2) cos71.6° )$ . Is this value correct? Check using the method for complex numbers in rectangular form. Is Kayslee's method applicable to any two complex numbers in the complex plane?
Coordinate Plane - 5x5 - With Dots

Yes, the value is correct, and Kayslee's method will work for all complex numbers (being careful with how the difference of arguments is calculated).
Yes, the value is correct, but this method only works in some instances.
Yes, the value is correct, but this is merely coincidence (there is no reason for it).
No, this value is not correct, and her method is also not correct (it does not correctly calculate the distance between complex numbers in the complex plane).