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The complex number is defined by w=(22+4i)/(2-i)². Show that w= 2+4i. How to solve this?

1 answers
Adeel AliI love math!17.5k students helped

Further Maths! <3 Okay so, you need to rationalise the the denominator. But before we do that we should square the complex number (2-i). (2-i)² gives you 3-4i. Now W = (22+4i)/(3-4i) To rationalise a complex number you multiply it by its conjugate pair. Therefore the conjugate pair to (3-4i) is (3+4i). (3-4i)(3+4i) = 25 (Oh look! A real number!) Since you multiplied the denominator by 3+4i it is only right we do the same to the numerator. So (22+4i)(3+4i) = 50 + 100i. Now W = (50 + 100i)/25 = (2 + 4i) as required hope this helps!

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