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Question

If z1=1+3i, z2=13i, then z1001+z1002z1+z2=

A
2100
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B
-2100
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C
299
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D
299
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Solution

The correct option is B 299
z1 =1+3i=2w

z2 =13i=2w2

We know , w2+w=1 and w3=1

=z1100+z2100z1+z2

=(2w)100+(2w2)1002w+2w2

=2100((w)100+(w2)100)2(w+w2)

=2100((w)+(w2))2(1)

=2100(1)2(1)

= 299

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