SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

  • Login
  • Get Help
  • About

Complex Numbers, SPEC2 2019 VCAA 4 MC

The expression  `i^(1!) + i^(2!) + i^(3!) + …+ i^(100!)`  is equal to

  1. `0`
  2. `96`
  3. `95 + i`
  4. `94 + 2i`
  5. `98 + 2i`
Show Answers Only

`C`

Show Worked Solution

`i^(1!) =i^1 =  i`

`i^(2!) =i^2= −1`

`i^(3!) = i^6=-1`

`i^(4!) = i^24 = 1`

`i^(5!) = i^(24 xx 5)= 1^5 = 1`

`=> i^(n!) = 1\ \ text(for)\ \ n >= 4`

`:.\ text(Sum)` `= i – 1 – 1 + 97`
  `= 95 + i`

 
`=>C`

Filed Under: Basic Calculations (SM) Tagged With: Band 5, smc-1171-30-Other

Copyright © 2014–2025 SmarterEd.com.au · Log in