Arithmetic/Types of Numbers/Complex Number

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Complex Number[edit]

Complex Number is a number that can be expressed mathematically as a sum of a Real Number and an Imaginary Number

Z = A + jB
Z = |Z|\angle \theta
|Z| = \sqrt{A^2 + B^2}
\theta = Tan^-1 \frac{B}{A}

Complex Conjugate Number[edit]

Z = A - jB
Z = |Z|\angle -\theta
|Z| = \sqrt{A^2 + B^2}
\theta = -Tan^-1 \frac{B}{A}

Rules[edit]

If there are two Complex Numbers

Z_1 = A + jB
Z_2 = C + jD


  1. (A + jB) + (C + jD) = (A + C) + j (B + D)
  2. (A + jB) - (C + jD) = (A - C) + j (B - D)
  3. (A + jB) x (C + jD) = (AC + BD) + j (AD + BC)
  4. \frac{(A + jB)}{(C + jD)} = \frac{(A + jB) (C - jD)}{(C+ jD) (C - jD)} = \frac{(AC + BD) + j (BC - AD)}{C^2 + D^2}



  1. Z_1 \times Z_2 = |Z_1| |Z_2| \angle (\theta_1 + \theta_2)
  2. Z_1 / Z_2 = \frac{|Z_1|}{|Z_2|} \angle (\theta_1 - \theta_2)