Standard +0.3 This is a standard FP1 technique for finding square roots of complex numbers by equating real and imaginary parts of (a+bi)² = 21-20i, leading to simultaneous equations. While it requires careful algebraic manipulation and solving a quadratic, it's a routine textbook exercise that FP1 students practice extensively, making it slightly easier than average overall A-level difficulty.
Attempt to equate real and imaginary parts of \((x+iy)^2\) and \(21-20i\)
A1A1
Obtain each result
M1
Eliminate to obtain a quadratic in \(x^2\) or \(y^2\)
M1
Solve to obtain \(x = (\pm)5\) or \(y = (\pm)2\)
\(\pm(5 - 2i)\)
A1
Obtain correct answers as complex numbers
Total: 6 marks
$x^2 - y^2 = 21$ and $xy = -10$ | M1 | Attempt to equate real and imaginary parts of $(x+iy)^2$ and $21-20i$
| A1A1 | Obtain each result
| M1 | Eliminate to obtain a quadratic in $x^2$ or $y^2$
| M1 | Solve to obtain $x = (\pm)5$ or $y = (\pm)2$
$\pm(5 - 2i)$ | A1 | Obtain correct answers as complex numbers
**Total: 6 marks**