Question

Need some help, kinda stuck

Answer 1

7/4

Explanation:

`\displaystyle(2 + √( - 3) )/(2) ( (2 - √( - 3) )/(2) )~~~~~~`

Evaluate.

Solution:

Rewrite it as,

• 
  `\displaystyle(2 + √( - 1 ) √( 3) )/(2) ( (2 - √( - 1) √(3) )/(2) )`
• 
  `\displaystyle(2 + i√( 3) )/(2) ( (2 - i√( 3) )/(2) )~~~~~~`

Multiplying them,

• 
  `\displaystyle((2 + i√( 3))*(2 - i √(3)) )/(2 * 2)`

• 
  `\displaystyle((2 + i√( 3))*(2 - i √(3)) )/(4)`

Applying Distributive property,

• 
  `\displaystyle(2(2 + i√( 3)) + \: i √(3) (2 - i √(3)) )/(4)`

• 
  `\cfrac{2 * 2 + 2( - i √(3) ) + i √(3)(2 - i √(3) ) }{4}`

• 
  `\cfrac{2 * 2 + 2( - i √(3)) + i √(3) * 2 + i √(3) ( - i √(3)) }{4}`

Combining each terms,

• 
  `\cfrac{4 - 2i √(3) + 2i √(3) + 3}{4}`
• 
  `\cfrac{ - 2i √(3) + 2i √(3) + 7 }{4}`
• 
  `\boxed{\cfrac{ 7}{4} }`

Last Choice is accurate.