Question 5
[Maximum number: 5]
The square roots of can be expressed in the Cartesian form x+iy, where x and y are real and exact.
By first forming a quartic equation in x or y, find the square roots of in exact Cartesian form.
CAIE A-Level Mathematics 3.9.6 Complex numbers
Practise finding exact square roots of complex numbers in Cartesian or polar form, showing the equations that determine both roots.
How this is tested
- square x+iy and equate real and imaginary parts to form two equations
- eliminate x or y to find exact Cartesian square roots in conjugate-sign pairs
- halve the argument and root the modulus when square roots are requested in polar form