Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The value of $i^{99}$ is
2. The multiplicative inverse of $2 - 3i$ is
3. The roots of the equation $x^2 + x + 1 = 0$ are
4. If $z = \bar{z}$, then $z$ is
5. The modulus of $(1+i)^4$ is
6. Express $(1-i)^4$ in the form $a+ib$.
7. Solve the quadratic equation $2x^2 + x + 1 = 0$.
8. Find the real values of $x$ and $y$ if $(x+iy)(2-3i) = 4+i$.
9. Evaluate $[i^{18} + (\frac{1}{i})^{25}]^3$.
10. Solve the equation $x^2 - 2x + \frac{3}{2} = 0$.
11. Convert the complex number $\frac{1+7i}{(2-i)^2}$ into standard form $a+ib$.
12. Case Study: A quadratic equation is given by $x^2 + 3x + 9 = 0$.
    (i) Find the discriminant of the equation.
    (ii) Determine the nature of the roots.
    (iii) Find the roots of the equation.