Theory of Intelligence
11TH•Mathematics•Complex Numbers•Exercise 1.2

Theory

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Theory

  • Complex multiplication: (a+bi)(c+di)=(ac−bd)+(ad+bc)i(a+bi)(c+di)=(ac-bd)+(ad+bc)i.
  • Use i2=−1i^2=-1.
  • To solve for x,yx,y in x+iy=α+iβx+iy=\alpha+i\beta, compare real and imaginary parts.
  • To simplify 1a+bi\dfrac{1}{a+bi}, multiply numerator and denominator by a−bia-bi.

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