Imaginary Common Ratio?

Algebra Level 1

True or false:

1+i+i2+i3+i4+ 1 + i + i^2 + i^3 + i^4 + \cdots

The expression above represents an infinite geometric progression sum with first term, a=1a = 1 and common ratio r=ir = i . And it can be expressed as a1r=11i=11i1+i1+i=1+i1i2=12+12i  . \dfrac a{1-r} =\dfrac 1{1-i} = \dfrac 1{1-i} \cdot \dfrac{1+i}{1+i} = \dfrac{1+i}{1-i^2} = \dfrac12 + \dfrac12 i \; .

Clarification: i=1i=\sqrt{-1}.

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