What is the absolute value of 7 + 12i?
(1 point)
Responses
Start Root 19 End Root
Image with alt text: Start Root 19 End Root
Start Root 193 End Root
Image with alt text: Start Root 193 End Root
19
19
193
193
The absolute value of 7 + 12i is the distance from the origin to the point represented by the complex number 7 + 12i in the complex plane. This can be found using the Pythagorean theorem.
The real part of the complex number is 7 and the imaginary part is 12.
The absolute value can be calculated as:
|7 + 12i| = √(7^2 + 12^2)
= √(49 + 144)
= √(193)
Therefore, the absolute value of 7 + 12i is √193.
To find the absolute value of a complex number, you need to find the distance from the origin (0, 0) to the point representing the complex number on the complex plane.
In this case, we have the complex number 7 + 12i.
To find the absolute value, you can use the formula:
|z| = sqrt(x^2 + y^2)
where z is the complex number, x is the real part, and y is the imaginary part.
So, for 7 + 12i, the real part is 7 and the imaginary part is 12.
|7 + 12i| = sqrt(7^2 + 12^2) = sqrt(49 + 144) = sqrt(193).
Therefore, the absolute value of 7 + 12i is sqrt(193).