Simplify 
(a + ib)^2/a-ib  - (a-ib)^2/(a+ib)

Asked by dalbirgolagarh | 8th Jul, 2016, 06:12: PM

Expert Answer:

begin mathsize 12px style fraction numerator left parenthesis straight a plus ib right parenthesis squared over denominator straight a minus ib end fraction minus fraction numerator left parenthesis straight a minus ib right parenthesis squared over denominator straight a plus ib end fraction
equals fraction numerator straight a squared plus 2 iab plus straight i squared straight b squared over denominator straight a minus ib end fraction minus fraction numerator straight a squared minus 2 iab plus straight i squared straight b squared over denominator straight a plus ib end fraction
equals fraction numerator straight a squared plus 2 iab minus straight b squared over denominator straight a minus ib end fraction minus fraction numerator straight a squared minus 2 iab minus straight b squared over denominator straight a plus ib end fraction
equals fraction numerator left parenthesis straight a squared plus 2 iab minus straight b squared right parenthesis left parenthesis straight a plus ib right parenthesis minus left parenthesis straight a squared minus 2 iab minus straight b squared right parenthesis left parenthesis straight a minus ib right parenthesis over denominator left parenthesis straight a minus ib right parenthesis left parenthesis straight a plus ib right parenthesis end fraction
equals fraction numerator straight a cubed plus 2 ia squared straight b minus ab squared plus ia squared straight b plus 2 straight i squared ab squared minus ib cubed minus left square bracket straight a cubed minus ia squared straight b plus 2 ia squared straight b plus 2 straight i squared ab squared minus ab squared plus ib cubed right square bracket over denominator left parenthesis straight a minus ib right parenthesis left parenthesis straight a plus ib right parenthesis end fraction
equals fraction numerator straight a cubed plus 2 ia squared straight b minus ab squared plus ia squared straight b plus 2 straight i squared ab squared minus ib cubed minus straight a cubed plus ia squared straight b minus 2 ia squared straight b minus 2 straight i squared ab squared plus ab squared minus ib cubed over denominator straight a squared plus straight b squared end fraction
equals fraction numerator 2 ia squared straight b minus 2 ib cubed over denominator straight a squared plus straight b squared end fraction
equals fraction numerator 2 ib left parenthesis straight a squared minus straight b squared right parenthesis over denominator straight a squared plus straight b squared end fraction end style

Answered by Rebecca Fernandes | 10th Jul, 2016, 09:36: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.