What is the square of the modulus of the complex number $$ 3+4 i $$ ? A. 25 B. 7 C. 10 D. 12

Question

UpStudy AI · Accepted Answer

To find the square of the modulus of the complex number $$ 3 + 4i $$, we first need to calculate the modulus itself.

The modulus of a complex number $$ a + bi $$ is given by the formula:

$$
|a + bi| = \sqrt{a^2 + b^2}
$$

For the complex number $$ 3 + 4i $$:

- $$ a = 3 $$
- $$ b = 4 $$

Now, we calculate the modulus:

$$
|3 + 4i| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
$$

Next, we need to find the square of the modulus:

$$
|3 + 4i|^2 = 5^2 = 25
$$

Thus, the square of the modulus of the complex number $$ 3 + 4i $$ is $$ 25 $$.

The answer is $$ \boxed{25} $$.
The square of the modulus of $$ 3 + 4i $$ is 25.

What is the square of the modulus of the complex number \( 3+4 i \) ? A. 25 B. 7 C. 10 D. 12