By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
How to determine the distance of a complex number
Complex numbers are a generalization from real numbers, whose expression are of the form a + i b, where a and b are the components of the real and imaginary components, respectively. The magnitude of complex numbers is determined by Pythagorean theorem, this is, the distance from the origin to the location of the number on the complex plane:
[tex]r = \sqrt{a^{2}+b^{2}}[/tex]
If we know that a = 4 and b = -1, then the magnitude of the complex number is:
[tex]r = \sqrt{4^{2}+(-1)^{2}}[/tex]
[tex]r = \sqrt{17}[/tex]
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
Remark
The statement presents several typing mistakes, correct form is shown below:
Which complex number has a distance of [tex]\sqrt{17}[/tex] from the origin on the complex plane?
A. 2 + i 15
B. 17 + i
C. 20 - i 3
D. 4 - i
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