Plot the complex number and find its absolute value.
-5 + 2i

A) $$| - 5 + 2 i | = \sqrt { - 1 }$$
B) $$| - 5 + 2 i | = \sqrt { 28 }$$
C) $$| - 5 + 2 i | = \sqrt { 29 }$$
D) $$| - 5 + 2 i | = \sqrt { 2 }$$
E) $$| - 5 + 2 i | = \sqrt { 9 }$$

Question

Plot the complex number and find its absolute value. ​
-5 + 2i
​
A)​ ​ $$| - 5 + 2 i | = \sqrt { - 1 }$$ 
B)​ ​ $$| - 5 + 2 i | = \sqrt { 28 }$$ 
C)​ ​ $$| - 5 + 2 i | = \sqrt { 29 }$$ 
D)​ ​ $$| - 5 + 2 i | = \sqrt { 2 }$$ 
E)​ ​ $$| - 5 + 2 i | = \sqrt { 9 }$$

Quizplus · Accepted Answer

We can plot -5+2i on the complex plane as seen below:

```
  | 
2i|    ●
  | 
  | 
  |
-----●-----
    -5
```
 
The absolute value (or modulus or magnitude) of a complex number is given by the distance from the origin to the point representing the complex number. Using the Pythagorean theorem, we can find that the distance from the origin to -5+2i is:

|-5+2i| = sqrt((-5)^2 + 2^2) = sqrt(25+4) = sqrt(29)

Therefore, |-5+2i| = sqrt(29), which is closest to option C.

Plot the Complex Number and Find Its Absolute Value ∣−5+2i∣=−1| - 5 + 2 i | = \sqrt { - 1 }∣−5+2i∣=−1​

Plot the Complex Number and Find Its Absolute Value $| - 5 + 2 i | = \sqrt { - 1 }$