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What is the modulus (absolute value) of -12+5i ? Don't round. If necessary, express your answer as a radical. |-12+5i|=

What is the modulus (absolute value) of −12+5i -12+5 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣−12+5i∣= |-12+5 i|=

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Transformations of absolute value functions: translations and reflectionsright chevron icon

Full solution

Q. What is the modulus (absolute value) of −12+5i -12+5 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣−12+5i∣= |-12+5 i|=
  1. Calculate Modulus: The modulus of a complex number a+bia + bi is given by the square root of the sum of the squares of its real part (a)(a) and its imaginary part (b)(b). In this case, the complex number is −12+5i-12 + 5i, so we need to calculate the square root of (−12)2+(5)2(-12)^2 + (5)^2.\newlineCalculation: ((−12)2+(5)2)=(144+25)=169\sqrt{((-12)^2 + (5)^2)} = \sqrt{(144 + 25)} = \sqrt{169}
  2. Find Square Root of Sum: After calculating the sum inside the square root, we find that 169\sqrt{169} is a perfect square, which means that the square root of 169169 is an integer.\newlineCalculation: 169=13\sqrt{169} = 13

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