SQUARE ROOTS OF COMPLEX NUMBERS

GENERAL EQUATION FOR NUMBERS CONTAINING IMAGINARY RADICALS (Part II)

Picture of an equation

Stanley Rabinowitz published the article how to find the square roots of complex numbers in the journal Mathematics and Informatics Quarterly, 3(1993)54-56 . By following the same approach as Rabinowitz I am showing how to obtain the general equations for numbers containing imaginary radicals of the type a + b√k where k is any number greater than 0. In addition, k is square free, i.e.,any squares are removed from under the square root sign. For example if k = −18 the square 9 is removed and its root placed outside the radical, √  , to give k = −2. This article follows Part I for General equation for the square roots of non complex numbers

Construction of the Equations

Two Examples

Example I:

1321 + 7392√−2

Find r

r = √13212 + 2×73922  = 10537

Find x then y  (note that √(a − r  )/2  gives a negative value).

x = 1321 + 10537     = 77
2   

y =     7392   = 48
2 × 77

Giving the answer

(77 + 48√−2)2


Example II:

7078 − 1190√−3

Find r

r = √70782 + 3×11902  = 7372

Find x then y  (note √(a − r  )/2 gives an negative value).

x = ±√7078 + 7372     = 85, −85
2           

y =   −1190    = −7, 7
2 × ±85

Giving the answers

(85 − 7√ −3)2 and ( − 85 + 7√ −3)2

This concludes Part II.
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Copyright © 2011 by Eddie N Gutierrez. E-Mail: Fiboguti89@Yahoo.com