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vampirchik [111]
2 years ago
15

Which complex number has a distance of (square root)17 from the origin on the complex plane?

Mathematics
2 answers:
tatuchka [14]2 years ago
5 0
<h2>Answer:</h2>

The complex number which has a distance of √17 from the origin to the complex plane is:

                     Option: D

                    4-i

<h2>Step-by-step explanation:</h2>

We know that the distance of a complex number of the form a+ib from the origin ( (0,0) or 0+0.i ) is given by:

\sqrt{a^2+b^2}

Hence, we will calculate this expression in each of the options and check which is equal to √17

A)

2+15\cdot i

Here a=2 and b=15

Hence,

\sqrt{a^2+b^2}=\sqrt{2^2+(15)^2}\\\\\sqrt{a^2+b^2}=\sqrt{4+225}\\\\\\\sqrt{a^2+b^2}=\sqrt{229}\neq \sqrt{17}

Option: A is incorrect.

B)

17+i

Here a=17 and b=1

Hence,

\sqrt{a^2+b^2}=\sqrt{(17)^2+1^2}\\\\\sqrt{a^2+b^2}=\sqrt{290}\neq \sqrt{17}

Hence, option: B is incorrect.

C)

20-3i

Here a=20 and b= -3

\sqrt{a^2+b^2}=\sqrt{(20)^2+(-3)^2}\\\\\sqrt{a^2+b^2}=\sqrt{409}\neq \sqrt{17}

Hence, option: C is incorrect.

D)

4-i

Here a=4 and b= -1

\sqrt{a^2+b^2}=\sqrt{(4)^2+(-1)^2}\\\\\sqrt{a^2+b^2}=\sqrt{17}

Hence, option: D is correct.

Dovator [93]2 years ago
3 0
We are asked in the problem to determine which among the points has a distance of sqrt 17 from the origin. We can get the distance of each through square root of (a2 + b2) from the standard from a + bi. The answer to this problem is D. 4-i 
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<u>Answer</u>

18 and 12


<u>Explanation</u>

Factor is a number or algebraic expression that divides another number or expression evenly that is with no remainder.

Odd number have few factors so the can't be the answer.

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