Find Absolute Values Of Complex Numbers Worksheet

Algebra 2
Real And Complex Numbers

Total questions - 6

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How Will This Worksheet on "Find Absolute Values of Complex Numbers" Benefit Your Student's Learning?

  • Helps visualize the position of complex numbers in the complex plane.
  • Demonstrates the magnitude of complex numbers in math and physics.
  • Assists in calculating roots and powers of complex numbers, essential for solving math problems.
  • Important in advanced math for analyzing functions, residues, and integrals.

How to Find Absolute Values of Complex Numbers?

  • A complex number is in the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.
  • To find the absolute value \( |a + bi| \), use the formula \( \sqrt{a^2 + b^2} \).
  • Square the real part \( a \) and the imaginary part \( b \), then add these squares together.
  • Finally, take the square root of the sum to determine the absolute value of the complex number.

Solved Example

Q. Find the absolute value.\newline9i|-9i|
Solution:
  1. Absolute Value Calculation: What is the absolute value of a+bia + bi? \newlinea+bi=a2+b2|a + bi| = \sqrt{a^2 + b^2}
  2. Expression Substitution: For 9i|-9i|, a=0a = 0 and b=9b = -9\newlineUse a+bi=a2+b2|a + bi| = \sqrt{a^2 + b^2} and substitute the values.\newline 9i=02+(9)2|-9i| = \sqrt{0^2 + (-9)^2}
  3. Expression Simplification: Simplify 02+(9)20^2 + (-9)^2.\newline 02+(9)20^2 + (-9)^2 =0×0+(9×(9)= 0 \times 0 + (-9\times (-9) \newline=0+81= 0 + 81 =81= 81
  4. Final Value Calculation: Simplify 81 \sqrt{81} to find the value of 9i |-9i| . 9i=81=92=9 |-9i| = \sqrt{81} = \sqrt{9^2} = 9
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About Worksheet

Algebra 2
Real And Complex Numbers

To find the absolute value of a complex number \( a + bi \), calculate the distance from the origin to the point \( (a, b) \) in the complex plane. This is done using the formula \( \sqrt{a^2 + b^2} \). The absolute value represents the magnitude of the complex number. We can use absolute values of a complex numbers calculator to easily compute this value.

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