Question

If x = 3 + 4i = 3 and y=3-4i then find the value of x cube + y cube divided by 2(X square + xy + Y square)

Answer 1

Answer:

- 10.636

Step-by-step explanation:

(x³ + y³)/(2 × (x² + xy + y²))

using

a³ + b³ = (a+b)³ -3ab(a+b)

a² + b² = (a+b)² - 2ab

= ( (x+y)³ - 3xy(x+y) ) / ( 2× ((x+y)²-xy))

now

x + y = 3 + 4i + 3-4i

=> x + y = 6

xy = (3 + 4i)(3 -4i)

(a+b)(a-b) = a² - b²

=> xy = 3² - (4i)²

=> xy = 9 - 16i²

i² = -1

=> xy = 9 - 16(-1)  

=> xy = 9 + 16

=> xy = 25

putting values of x + y & xy in

( (x+y)³ - 3xy(x+y) ) / ( 2× ((x+y)²-xy))

= (6³ -3×25×6) / (2 × (6² - 25))

= (216 - 450) / (2 × (36 - 25))

= -234 / (2 × 11)

= -117 / 11

= - 10.636

Answer 2

Answer:

Hope this will help u mate.