A-LevelMathematicsComplex numbers9709/32 · May/June 2021 · Q55 Marks
The complex number u is given by u = 10 – 4√6i. Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and exact.
- The complex number u is given by u = 10 – 4√6i. Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and exact.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Square a + ib, use i² = −1 and equate real and imaginary parts to 10 and −4√6 respectively
- [A1] Obtain a²−b² = 10 and 2ab = −4√6
- [M1] Eliminate one unknown and find an equation in the other
- [A1] Obtain a⁴−10a²−24[= 0], or b⁴+10b²−24[= 0], or 3-term equivalent
- [A1] Obtain final answers ±(2√3−√2i), or exact equivalents
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →