Express the given complex number in the form displaystyle a-ib-left- dfrac - 1 - 5 - -idfrac - 2 - 5 - right- -left- 4-idfrac - 5 - 2 - right-

Question

Toppr Admin · Accepted Answer

-15-i25-x2212-4-i52-15-25i-x2212-4-x2212-52i-15-x2212-4-i-25-x2212-52-x2212-195-i-x2212-2110-x2212-195-x2212-2110i-a-ib- where a-x2212-195-b-x2212-2110

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

$(\frac{1}{5} + i \frac{2}{5}) - (4 + i \frac{5}{2})$
$= \frac{1}{5} + \frac{2}{5} i - 4 - \frac{5}{2} i$
$= (\frac{1}{5} - 4) + i (\frac{2}{5} - \frac{5}{2})$
$= \frac{- 19}{5} + i (\frac{- 21}{10})$
$= \frac{- 19}{5} - \frac{21}{10} i$
$= a + i b,$ where $a = - \frac{19}{5}, b = - \frac{21}{10}$

Express the given complex number in the form a+ib:(15+i25)−(4+i52)

(15+i25)−(4+i52)=15+25i−4−52i=(15−4)+i(25−52)=−195+i(−2110)=−195−2110i=a+ib, where a=−195,b=−2110

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

$(\frac{1}{5} + i \frac{2}{5}) - (4 + i \frac{5}{2})$
$= \frac{1}{5} + \frac{2}{5} i - 4 - \frac{5}{2} i$
$= (\frac{1}{5} - 4) + i (\frac{2}{5} - \frac{5}{2})$
$= \frac{- 19}{5} + i (\frac{- 21}{10})$
$= \frac{- 19}{5} - \frac{21}{10} i$
$= a + i b,$ where $a = - \frac{19}{5}, b = - \frac{21}{10}$