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Question

Express the complex number $$\dfrac{2+i}{3-4i}$$ in $$a+ib$$ form.


Solution

Given the complex number is 

$$\dfrac{2+i}{3-4i}$$ $$=\dfrac{(2+i)(3+4i)}{3^2-16i^2}$$

$$=\dfrac{2+11i}{25}$$

$$=\dfrac{2}{25}+i\dfrac{11}{25}$$.

This is the required $$a+ib$$ form.

Mathematics

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