Question

Express the given complex number in the form $a + ib: (\dfrac{1}{5}+i\dfrac{2}{5})-(4+i\dfrac{5}{2})$

Answer 1

$(\dfrac{1}{5}+i\dfrac{2}{5})-(4+i\dfrac{5}{2})$

$=(\dfrac{1}{5}-4)+i(\dfrac{2}{5})-\dfrac{5}{2})$

$=-\dfrac{19}{5}+i(\dfrac{-21}{10})$

$=-\dfrac{19}{5}-\dfrac{21}{10}i$ (Ans.)