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What is the modulus (absolute value) of 15+8i ? Don't round. If necessary, express your answer as a radical. |15+8i|=

What is the modulus (absolute value) of 15+8i 15+8 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣15+8i∣= |15+8 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 15+8i 15+8 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣15+8i∣= |15+8 i|=
  1. Complex number definition: 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 15+8i15 + 8i, so we have a=15a = 15 and b=8b = 8.
  2. Modulus formula: We calculate the modulus using the formula ∣a+bi∣=a2+b2|a + bi| = \sqrt{a^2 + b^2}. Substituting a=15a = 15 and b=8b = 8, we get ∣15+8i∣=152+82|15 + 8i| = \sqrt{15^2 + 8^2}.
  3. Substituting values: Now we calculate the squares of the real and imaginary parts: 152=22515^2 = 225 and 82=648^2 = 64.
  4. Calculating squares: We add these squares together: 225+64=289225 + 64 = 289.
  5. Summing squares: Finally, we take the square root of the sum to find the modulus: 289=17\sqrt{289} = 17.

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