if ( 1+ iota /1- iota) ^3- ( 1- iota/1+ iota) ^3 = x+iota y then find the value of (x,y)
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Answers
Given : {(1 + i)/(1 - i) }³ - {(1 - i)/(1 + i) }³ = x + iy
To find : x & y
Solution:
{(1 + i)/(1 - i) }³ - {(1 - i)/(1 + i) }³ = x + iy
{(1 + i)/(1 - i) }³ - {(1 - i)/(1 + i) }³
(1 + i)/(1 - i) = a
=> (1 - i)/(1 + i) = 1/a
a³ - 1/a³
a³ - b³ = (a - b)³ + 3ab(a - b)
= (a - 1/a)³ + 3(a.1/a)(a - 1/a)
= (a - 1/a)³ + 3(a - 1/a)
a - 1/a = (1 + i)/(1 - i) - (1 - i)/(1 + i)
= ( ( 1 + i)² - (1 - i)² ) /(1 - i²)
= ( 1 + i² + 2i - ( 1 + i² - 2i) )/ (1 -(-1))
= 4i/2
= 2i
(a - 1/a)³ + 3(a - 1/a) = (2i)³ + 3(2i)
= -8i + 6i
= - 2i
- 2i = x + iy
=> x = 0
y = - 2
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Answer:
x+y = -2
Step-by-step explanation:
Hope it will help you!!!!
