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The trick with complex fractions is to convert the complex denominators into real numbers, that is, remove any imaginary components. By doing this the whole fraction can be converted into a complex number which is now “rationalised”.

Take a general complex fraction: (a+ib)/(c+id), where a, b, c and d are real numbers. We need to get rid of c+id, so we multiply by (c-id)/(c-id).

The denominator becomes c²+d², while the numerator becomes:

(a+ib)(c-id)=ac+bd+i(bc-ad), so the real part of the fraction is (ac+bd)/(c²+d²) and the imaginary part is i(bc-ad)/(c²+d²).

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