Exercises: Norm, Conjugation, and Inversion of Complex Numbers

Problem 1

Evaluate and/or simplify the following expressions.

  1. \(\CAbs{ i\cdot (2+i) }\)

  2. \(\CAbs{ (1-i)\cdot (3-4i) }\)

Problem 2

Evaluate and/or simplify the following expressions.

  1. \(\CCnjgt{ -2(1-i)^3 + 2(1-i)^2 - 3(1-i) +1 }\)

  2. \(\CCnjgt{ (2+2i)(2-2i) }\)

  3. \(\CCnjgt{ 2(-1+2i)^2 + 3(2-i)(2+i) }\)

  4. \[\dfrac{ 2i }{ 1-i }\]
  5. \[\dfrac{ 1+i }{ 1-i }\]
  6. \[\CCnjgt{ \left( \dfrac{6i}{2-i} \right) }\]
  7. \[\dfrac{1+i}{2-i} + \dfrac{1+2i}{2+i}\]