Verify that $$$-1+\sqrt{2} \mathrm{i}$$$ is a root of the equation $$$z^{4}+3 z^{2}+2 z+12=0$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_33 Year：2021 Question No：10(a)

Answer:

Substitute $-1+\sqrt{2} i$ and attempt expansions of the $z^{2}$ and $z^{4}$ terms
Use $i^{2}=-1$ at least once
Complete the verification correctly

Knowledge points:

3.9.2 carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form (For calculations involving multiplication or division, full details of the working should be shown.)

Answer:

Knowledge points:

Solution:

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