Complex Analysis: Theory and Applications · Problem 4.1.11

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · series-scalar-multiplication

Problem

Let ∑n=1∞(xn+iyn)=u+iv\displaystyle\sum_{n=1}^{\infty}(x_n + iy_n) = u + iv. If c=a+ibc = a + ib is a complex constant, show that ∑n=1∞(a+ib)(xn+iyn)=(a+ib)(u+iv).\sum_{n=1}^{\infty}(a+ib)(x_n + iy_n) = (a+ib)(u+iv).

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