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What is the modulus (absolute value) of -24-7i ? Don't round. If necessary, express your answer as a radical. |-24-7i|=

What is the modulus (absolute value) of −24−7i -24-7 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣−24−7i∣= |-24-7 i|=

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Absolute values of complex numbersright chevron icon

Full solution

Q. What is the modulus (absolute value) of −24−7i -24-7 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣−24−7i∣= |-24-7 i|=
  1. Calculate Modulus of Complex Number: The modulus (absolute value) of a complex number a+bia + bi is given by the square root of the sum of the squares of its real part aa and its imaginary part bb. In this case, the complex number is −24−7i-24 - 7i, so we need to calculate the square root of (−24)2+(−7)2(-24)^2 + (-7)^2.
  2. Square the Real Part: First, we square the real part, which is −24-24. (−24)2(-24)^2 equals 576576.
  3. Square the Imaginary Part: Next, we square the imaginary part, which is −7-7. (−7)2(-7)^2 equals 4949.
  4. Add Squares of Real and Imaginary Parts: Now, we add the squares of the real and imaginary parts together: 576+49576 + 49 equals 625625.
  5. Take Square Root of Sum: Finally, we take the square root of the sum to find the modulus: 625\sqrt{625} equals 2525.

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