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The Complex Number System Solutions

• The complex number system consists of numbers in the form $\underline{\mathbf{ }\mathbf{ }\mathbf{ }\mathit{a}\mathbf{+}\mathit{b}\mathit{i}\mathbf{ }\mathbf{ }}$, where a and b are part of the     real    number system, or $a\in \mathrm{ℝ}, b\in \mathrm{ℝ}$.
•    Complex numbers ℂ    includes the set of real numbers ℝ, and the set of imaginary numbers i.
• The number i can only be combined with    like terms   , meaning other imaginary numbers.
• This means that a real number and an imaginary number can only be written as an    expression   .
  •    Real numbers    are written as $a+bi$ where $b=0$ (or a).
  •    Pure imaginary numbers    numbers are written as $a+bi$ where $a=0$ (or bi).

Example 6

Classify by all sets to which it belongs: real, pure imaginary, complex. Then add A–D to the Complex Number diagram on the previous page.