What is the absolute value of negative 4 minus 9 i?
(1 point)
Responses
negative 13
Image with alt text: negative 13
5
5
Start Root 65 End Root
Image with alt text: Start Root 65 End Root
Start Root 97 End Root
Image with alt text: Start Root 97 End Root
To find the absolute value of a complex number, we need to calculate the magnitude or distance from the origin.
The absolute value of a complex number a + bi is given by:
|a + bi| = √(a^2 + b^2)
In this case, the complex number is -4 - 9i.
| -4 - 9i | = √((-4)^2 + (-9)^2)
= √(16 + 81)
= √97
Therefore, the absolute value of -4 - 9i is √97.
To find the absolute value of a complex number, you need to find the distance between that number and the origin (0,0) on a complex plane.
In this case, the complex number is -4 - 9i.
To find the distance between the complex number and the origin, you can use the formula:
|a + bi| = √(a^2 + b^2)
Plugging in the values from the given complex number, we get:
|-4 - 9i| = √((-4)^2 + (-9)^2)
= √(16 + 81)
= √97
Therefore, the absolute value of -4 - 9i is √97.