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Absolute Value of a Complex Number: The absolute value of a complex number a + bi is |a + bi| = Ö (a2 + b2)

When comes to calculating one or more complex numbers, we use the following formulas:

Addition of Complex Numbers: For all real numbers a, b. c, and d, (a + bi) + (c + di) = (a + c) + (b + d)i.

The Additive Inverse Property of Complex Numbers: For each complex number z, there is a complex number - z such that z + ( - z) = 0. If z = a + bi, then - z = - (a + bi) = - a - bi.

Subtraction of Complex Numbers: For all complex numbers w and z, w - z = w + (- z).

If w = a + bi and z = c + di, then w - z = (a + bi) - (c + di) = (a – c) + (b + d)i

Complex Conjugates: For all real numbers a and b, a + bi and a - bi are complex conjugates.

Multiplication of Complex Numbers: For all complex numbers a + bi and c + di, (a + bi)(c + di) = (ac - bd) + (ad + bc)i.

Quadratic equations are very useful in solving many problems and equations.  If you can learn quadratic equations well, you will do well on all kinds of problems.   Please take a few minutes break and click here to continue to the next chapter. (You can also click on the drop-down list below to jump to any chapter you like.)

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