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Complex Numbers

"Complex" numbers share many properties with the real numbers. In fact, complex numbers include all the real numbers, so you know lots of them already. Such an overachiever.

Complex Numbers Warmup

         

True or False:

For complex numbers \(a\) and \(b\),

\[ |a| + |b| = |a+b|. \]

Evaluate

\[ i \times ( -i) . \]

Note: \(i \) is the imaginary unit, where \(i^2=-1\).

For any complex number \(z\), which of the following must be equal to

"the real part of the imaginary part of \(z\)"?

Which of the following is equal to

\[ \frac{ 1 + i } { 1 - i }? \]

Are real numbers also complex numbers?

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