What is the modulus (absolute value) of 7+3i ? Don't round. If necessary, express your answer as a radical. |7+3i|=◻

Calculate modulus of complex number: The modulus (absolute value) of a complex number a + bi is given by the square root of the sum of the squares of its real part (a) and its imaginary part (b). So, for the complex number 7 + 3i, we need to calculate the square root of (7^2 + 3^2).Square the real part: First, we square the real part, which is 7. So, 7^2 equals 49.Square the imaginary part: Next, we square the imaginary part, which is 3. So, 3^2 equals 9.Add squares of real and imaginary parts: Now, we add the squares of the real and imaginary parts together. This gives us 49 + 9, which equals 58.Take square root of the sum: Finally, we take the square root of 58 to find the modulus of 7 + 3i. Since 58 is not a perfect square, we leave it under the radical as √58.

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Absolute values of complex numbers

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Q. What is the modulus (absolute value) of

7+3 i

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Don't round. If necessary, express your answer as a radical.

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|7+3 i|=\square

Calculate modulus of complex number: The modulus (absolute value) of a complex number $a + bi$ is given by the square root of the sum of the squares of its real part ( $a$ ) and its imaginary part ( $b$ ). So, for the complex number $7 + 3i$ , we need to calculate the square root of $(7^2 + 3^2)$ .
Square the real part: First, we square the real part, which is $7$ . So, $7^2$ equals $49$ .
Square the imaginary part: Next, we square the imaginary part, which is $3$ . So, $3^2$ equals $9$ .
Add squares of real and imaginary parts: Now, we add the squares of the real and imaginary parts together. This gives us $49 + 9$ , which equals $58$ .
Take square root of the sum: Finally, we take the square root of $58$ to find the modulus of $7 + 3i$ . Since $58$ is not a perfect square, we leave it under the radical as $\sqrt{58}$ .