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Algebra
 Imaginary Expression
 Sources and References

Algebra

Imaginary Expression

The following are conventions: That √(βˆ’π‘Ž2) is equivalent to π‘Žβˆš(βˆ’1); that π‘Žβˆš(βˆ’1) vanishes when π‘Ž vanishes; that the symbol π‘Žβˆš(βˆ’1) is subject to the ordinary rules of Algebra. √(βˆ’1) is denoted by 𝑖.223 If 𝛼+𝑖𝛽=𝛾+𝑖𝛿; then 𝛼=𝛾 and 𝛽=𝛿.224 𝛼+𝑖𝛽 and π›Όβˆ’π‘–π›½ are conjugate expressions; their product=𝛼2+𝛽2.225 The sum and product of two conjugate expressions are both real, but their difference is imaginary.226 The modulus is +𝛼2+𝛽2.227 If the modulus vanishes, 𝛼 and 𝛽 must vanish.228 If two imaginary expressions are equal, their moduli are equal, by (224).229 The modulus of the product of two imaginary expressions is equal to the product of their moduli.230 Also the modulus of the quotient is equal to the quotient of their moduli.231

Sources and References

https://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive

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ID: 210600017 Last Updated: 6/17/2021 Revision: 0 Ref:

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References

  1. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science & Engineering
  2. Wheatstone, C., 1854, On the Formation of Powers from Arithmetical Progressions
  3. Stroud, K.A., 2001, Engineering Mathematics
  4. Coolidge, J.L., 1949, The Story of The Binomial Theorem
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