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What is the modulus (absolute value) of
6-8i ?
Don't round. If necessary, express your answer as a radical.

|6-8i|=

What is the modulus (absolute value) of $6-8 i$ ? $\newline$ Don't round. If necessary, express your answer as a radical. $\newline$ $|6-8 i|=$

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Evaluate powers with negative or zero exponents

Full solution

Q. What is the modulus (absolute value) of

6-8 i

?

\newline

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

\newline

|6-8 i|=

Understanding the modulus: Understand the modulus of a complex number. The modulus 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 ( $b$ ). In mathematical terms, $|a + bi| = \sqrt{a^2 + b^2}$ . For the complex number $6 - 8i$ , $a = 6$ and $b = -8$ .
Calculating squares: Calculate the squares of the real and imaginary parts. $\newline$ Square the real part: $6^2 = 36$ . $\newline$ Square the imaginary part: $(-8)^2 = 64$ .
Adding squares: Add the squares of the real and imaginary parts. $\newline$ Sum of the squares: $36 + 64 = 100$ .
Finding the modulus: Take the square root of the sum to find the modulus. The square root of $100$ is $10$ . Therefore, the modulus of $6 - 8i$ is $10$ .

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