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Worked solution

Relate real numbers to complex numbers

What is the relation between the set of real numbers and the set of complex numbers?

CJC · Lecture · Opening activity

Answer

The real numbers form a subset of the complex numbers: R⊂C\mathbb R\subset\mathbb C. In fact it is a proper subset.

Compare your reasoning

Every real number a is also the complex number a+0ia+0i. But i is complex and not real. This completes both Teacher blanks: “subset” and R⊂C\mathbb R\subset\mathbb C. In the source nesting, N⊂Z⊂Q⊂R⊂C\mathbb N\subset\mathbb Z\subset\mathbb Q\subset\mathbb R\subset\mathbb C; the real numbers include both rational and irrational values.

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