Theory of Intelligence
11TH•Mathematics•Complex Numbers•Exercise 1.5

Theory

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Theory

  • If arg⁡(w)=π4\arg(w)=\frac{\pi}{4}, then tan⁡arg⁡(w)=1\tan\arg(w)=1 and (when Re⁡(w),Im⁡(w)\operatorname{Re}(w),\operatorname{Im}(w) have the same sign):
Im⁡(w)=Re⁡(w)\operatorname{Im}(w)=\operatorname{Re}(w)
  • To simplify a complex fraction a+bic+di\dfrac{a+bi}{c+di}, multiply numerator and denominator by c−dic-di.

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