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What is the modulus (absolute value) of -6+4i ? Don't round. If necessary, express your answer as a radical. |-6+4i|=

What is the modulus (absolute value) of −6+4i -6+4 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣−6+4i∣= |-6+4 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 −6+4i -6+4 i ?\newlineDon't round. If necessary, express your answer as a radical.\newline∣−6+4i∣= |-6+4 i|=
  1. Calculate 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 −6+4i-6 + 4i, so we need to calculate the square root of (−6)2+(4)2(-6)^2 + (4)^2.
  2. Square the real part: First, we square the real part: (−6)2=36(-6)^2 = 36.
  3. Square the imaginary part: Next, we square the imaginary part: (4)2=16(4)^2 = 16.
  4. Add squares of real and imaginary parts: Now, we add the squares of the real and imaginary parts: 36+16=5236 + 16 = 52.
  5. Take square root of sum: Finally, we take the square root of the sum to find the modulus: 52\sqrt{52}. Since 5252 is not a perfect square, we leave the answer as a radical.

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