Answer:
4(3)+0.95=X
Step-by-step explanation:
(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)
… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)
… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))
… = (2 - 2√3 <em>i</em> ) / 4
… = 1/2 - √3/2 <em>i</em>
… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))
… = exp(<em>i</em> arctan(-√3))
… = exp(-<em>i</em> arctan(√3))
… = exp(-<em>iπ</em>/3)
By DeMoivre's theorem,
[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1
The appropriate formula here is l = a + (n-1)d, where l represents the last term.
Here the first term is -5 and the common difference is +4. Thus,
l = -5 + (n-1)(4) (answer)
Check: we are given the arith sequence -5, -1, 3, 7. Does our formula correctly predict the 1st term? l = -5 + (1-1)(4) = > -5. Yes.
Does it correctly predict the 3rd term? l = -5 +(3-1)(4) => -5+2(4) = 3. Yes
