First slide

Algebra of complex numbers

Question

If $a + i b = \sum_{k = 1}^{101} i^{k},$ then $(a, b)$ equals

Easy

A

$(0, 1)$
B

$(0, 0)$
C

$(0, - 1)$
D

$(1, 1)$

Solution

Write
$\begin{matrix} a + i b = i + (i^{2} + i^{3} + i^{4} + i^{5}) + (i^{6} + i^{7} + i^{8} + i^{9}) \\ + \dots (i^{98} + i^{99} + i^{100} + i^{101}) \end{matrix}$

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