Moderate -0.3 This is a standard FP1 technique requiring students to set √(15+8i) = a+bi, square both sides, equate real and imaginary parts, then solve the resulting simultaneous equations. While it's a Further Maths topic (making it harder than typical A-level), it's a routine textbook exercise with a well-practiced method and straightforward arithmetic, placing it slightly below average difficulty overall.
Attempt to equate real and imaginary parts of \((x + iy)^2\) and \(15 + 8i\)
A1 A1
Obtain each result
M1
Eliminate to obtain a quadratic in \(x^2\) or \(y^2\)
A1
Solve to obtain \(x = (\pm)4\), or \(y = (\pm)1\)
Obtain only correct two answers as complex numbers: \(\pm(4 + i)\)
$x^2 - y^2 = 15$ and $xy = 4$ | M1 | Attempt to equate real and imaginary parts of $(x + iy)^2$ and $15 + 8i$
| A1 A1 | Obtain each result
| M1 | Eliminate to obtain a quadratic in $x^2$ or $y^2$
| A1 | Solve to obtain $x = (\pm)4$, or $y = (\pm)1$
| | Obtain only correct two answers as complex numbers: $\pm(4 + i)$