Question 99744
problem 1: 3/sqrt2-5i (i is for imaginary number) 

= (3(sqrt(2)+5i)/[sqrt(2)-5i)(sqrt(2)+5i)]

= [3(sqrt(2)+5i)] / [2+25]

= (sqrt(2)+5i)/9

= (1/9)sqrt(2)+(5/9)i

------------------------------------

problem 2: divide (1+i) by (2-i). Write the result in standard form. (i is for imaginary number)
(1+i)/(2-i)

= [(1+i)(2+i)]/[(2-i)(2+i)] 

= [1+3i]/[4+1]

= (1/5)+(3/5)i

--------------------------------


problem 3: perform the operation and write the result in standard form: 
(5-sqrt4)^2
= 25+4 -2*5*sqrt4

= 29 - 20

= 9
============================
Cheers,
Stan H.