(a) 10+10i=102cis(π/4). The five roots are zk=(102)1/5cis(20π+52kπ),k=0,1,2,3,4.
(b) The common modulus is (102)1/5≈1.698646. Among the five arguments, k=0 has the greatest cosine. Therefore z0=(102)1/5[cos(π/20)+isin(π/20)]≈1.678+0.266i.
Expresses the right side in polar form.
[1 mark]
Determines the root modulus.
[1 mark]
Determines all five arguments.
[2 marks]
Identifies the correct root.
[1 mark]
Gives its Cartesian approximation.
[1 mark]
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.