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Question Number 14011 by Ruth1 last updated on 26/May/17

$$\mathrm{simplify}:\frac{4-\mathrm{j}5}{1+\mathrm{j}2}$$

Commented by tawa tawa last updated on 26/May/17

$$\mathrm{Multiply}\mathrm{by}\mathrm{the}\mathrm{conjugate}\mathrm{both}\mathrm{numerator}\mathrm{and}\mathrm{denominator}$$$$\frac{(4-\mathrm{j}5)}{(1+\mathrm{j}2)}\times \frac{(1-\mathrm{j}2)}{(1-\mathrm{j}2)}$$$$=\frac{4-\mathrm{j}8-\mathrm{j}5+{10\mathrm{j}}^2}{1^2-{4\mathrm{j}}^2}$$$$=\frac{4-\mathrm{j}8-\mathrm{j}5+10(-1)}{1^2-4(-1)}[{\mathrm{j}}^2=-1]$$$$=\frac{4-\mathrm{j}8-\mathrm{j}5-10}{1+4}$$$$=\frac{-6-\mathrm{j}13}{5}$$$$=\frac{-6}{5}-\mathrm{j}\frac{13}{5}$$$$=-1.2-\mathrm{j}2.6$$

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