| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | January |
| Marks | 11 |
| Topic | Complex Numbers Arithmetic |
| Type | Square roots with follow-up application |
| Difficulty | Standard +0.3 Finding square roots of complex numbers algebraically is a standard Further Maths technique (setting √(16+30i) = a+bi and solving), and part (ii) is a straightforward application using the quadratic formula. Both parts follow routine procedures with no novel insight required, making this slightly easier than average. |
| Spec | 4.02h Square roots: of complex numbers4.02i Quadratic equations: with complex roots |
7.\\
(i) Use an algebraic method to find the square roots of the complex number $16 + 30 \mathrm { i }$.\\
(ii) Use your answers to part (i) to solve the equation $z ^ { 2 } - 2 z - ( 15 + 30 \mathrm { i } ) = 0$, giving your answers in the form $x + \mathrm { i } y$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q7 [11]}}