SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

  • Login
  • Get Help
  • About

Complex Numbers, SPEC2 2020 VCAA 8 MC

Given that  `(x + iy)^14 = a + ib`, where  `x, y, a, b ∈ R, \ (y - ix)^14`  for all values of `x` and `y` is equal to

  1. `−a - ib`
  2. `b - ia`
  3. `−b + ia`
  4. `−a + ib`
  5. `b + ia`
Show Answers Only

`A`

Show Worked Solution

♦♦ Mean mark 34%.
`(y – ix)^14` `= (−i(x + iy))^14`
  `= −i^14(x + iy)^14`
  `= −(x + iy)^14`
  `= −a – ib`

 
`=>A`

Filed Under: Basic Calculations (SM) Tagged With: Band 5, smc-1171-20-Powers

Complex Numbers, SPEC2 2014 VCAA 6 MC

Given that  `i^n = p`  and  `i^2 = −1`, then  `i^(2n + 3)`  in terms of `p` is equal to

  1. `p^2 - i`
  2. `p^2 + i`
  3. `−p^2`
  4. `−ip^2`
  5. `ip^2`
Show Answers Only

`D`

Show Worked Solution
`i^(2n + 3)` `= i^(2n)i^2i`
  `= (i^n)^2i^2i`
  `= −ip^2`

 
`=> D`

Filed Under: Basic Calculations (SM) Tagged With: Band 4, smc-1171-20-Powers

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