College Algebra Complex Numbers Operations with Complex Numbers
Division Concepts 1

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Let z1=x1+iy1 and z2=x2+iy2 and z2 is nonzero complex number. Then the quotient is given by

Example 1. If z1 = 2 + 3i and z2 = 4 + 5i, find .
Solution
We have x1 = 2, y1 = 3, x2 = 4, y2 = 5.
Hence, by definition,

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To express as a single complex number the quotient of one complex number as z1=x1+iy1 by another complex number, as z2=x2+iy2 , where z2 does not equal 0, multiply both numerator and denominator of the indicated quotient by x2 - iy2 , the conjugate of the denominator:
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Illustration (compare with Example 1). If z1 = 2 + 3i and z2 = 4 + 5i , find .

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Conjugate of the Quotient of Complex Numbers The conjugate of the quotient of complex numbers equals to the quotient of the conjugate of these complex numbers. In formula

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