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

What is the modulus (absolute value) of 7−i 7-i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣7−i∣= |7-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 7−i 7-i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣7−i∣= |7-i|=
  1. Modulus of Complex Number: 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 (aa) and its imaginary part (bb). In this case, the complex number is 7−i7 - i, where the real part is 77 and the imaginary part is −1-1.\newlineCalculation: ∣7−i∣=72+(−1)2=49+1=50|7 - i| = \sqrt{7^2 + (-1)^2} = \sqrt{49 + 1} = \sqrt{50}
  2. Calculation of Modulus: The square root of 5050 can be simplified by factoring out the square root of a perfect square that is a factor of 5050. The largest perfect square factor of 5050 is 2525.\newlineCalculation: 50=(25×2)=25×2=52\sqrt{50} = \sqrt{(25 \times 2)} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}

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