Question

find the value of (3+2/i)(i6-i7)(1+i11)
$5 \times 5(86)$
​

Answer 1

Answer:

(3 + 2 / i)(i^6 - i^7)(1 + i^11) = 6i + 4

Step-by-step explanation:

we are given that

  (3 + 2 / i)(i^6 - i^7)(1 + i^11)

= (3 + 2i / i²)(i^6 - i^7)(1 + i^11)

= (3 - 2i)(-1 + i)(1 - i)            ∵  i^6 = -1 , i^7 = -i , i^11 = -i , i² = -1

= (3 - 2i)(-1)(1 - i)(1-i)

= ( 2i - 3 )(1 - i)²

= ( 2i - 3 )(1² - 2i + i²)

= ( 2i - 3 )(1 - 2i - 1)         ∵ i² = -1

= ( 2i - 3 )(- 2i )

= 6i - 4i²         ∵ i² = -1

= 6i + 4

Hence

(3 + 2 / i)(i^6 - i^7)(1 + i^11) = 6i + 4