Schaum's Outline of Intermediate Algebra by Ray Steege

Author:Ray Steege
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2018-10-22T16:00:00+00:00

Pure imaginary numbers are merely complex numbers whose real part is zero. No pure imaginary number is a member of the set of real numbers. Therefore, the set of real numbers, R, is a proper subset of the set of complex numbers C. That is, R ⊂ C.

If b is an irrational number in the a + bi expression, we write the i factor first. We write 3 + i rather than 3 + i in order to avoid ambiguity. Hence, the complex number form is sometimes a + ib.

See solved problem 5.22.

Definition 11. a + bi = c + di if and only if a = c and b = d.

The above definition states that two complex numbers are equal if and only if their real parts are the same and their imaginary parts are the same also.

We shall now consider operations on complex numbers.

Addition: (a + bi) + (c + di) = (a + c) + (b + d)i

Subtraction: (a + bi) – (c + di) = (a – c) + (b – d)i

To add or subtract complex numbers, simply add or subtract their real parts and their imaginary parts, respectively.

See solved problem 5.23.

We multiply complex numbers as if they were two binomials. That is, distribute. You may use the FOIL method. Read the following sequence of statements.

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