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 `−a - ib` `b - ia` `−b + ia` `−a + ib` `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`
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 `p^2 - i` `p^2 + i` `−p^2` `−ip^2` `ip^2` Show Answers Only `D` Show Worked Solution `i^(2n + 3)` `= i^(2n)i^2i` `= (i^n)^2i^2i` `= −ip^2` `=> D`