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The division of two complex numbers arithematic operation requires the use of complex conjugate?
Wiki User
∙ 12y ago
(3+2i)/(5+4i)
If you multiply both sides by the conjugate of the denominator (5-4i), you get:
(3+2i)(5-4i)/(5+4i)(5-4i)
= (23-2i)/(25 + 16 +20i - 20i)
= (23-2i)/41
The denominator is now real, because the i terms cancel
As a general formula (easy to expand) this would be:
(a+bi)/(c+di) = [(ac+bd) + (bc-ad)i] / (c^2 + d^2)
It's a very easy method, but if you're the sort of person who loves using general formulas, there it is.
Wiki User
∙ 12y ago
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