Simplify -rationalizing the denominator.

Question

(5√2)/(2-i) by rationalizing the denominator.

Answer 1

Given 5sqrt(2)/(2-i)

Multiply numerator and denominator with (2+i)

= (5sqrt(2)*(2+i))/((2-i)(2+i))

Recall : (a+b)*(a-b) = a^2-b^2

= (5sqrt(2)*(2+i))/(2^2-i^2)

= 5sqrt(2)*2+5sqrt(2)*i)/(4-i^2)         { since i^2 = -1 }

= 10sqrt(2)+5sqrt(2)i/(4+1)

=  10sqrt(2)+5sqrt(2)i/5

Taking 5 common from numerator

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

= 2sqrt(2)+isqrt(2)

Answer 2

Given that

Rationalize the denominator

Take common 5 from numerator and denominator