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Question

If z=2+23 i, then z2n+22nzn+24n may be equal to

A
342n
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B
22n
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C
242n
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D
0
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Solution

The correct options are
A 342n
D 0
ω=1+3i2
z=2+23 i=4ω

z2n+22nzn+24n=(4ω)2n+22n(4ω)n+24n
=42nω2n+22n4nωn+24n
=42n[ω2n+ωn+1]
={0 , if n is not a multiple of 3342n , if n is a multiple of 3

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