Imaginary Common Ratio?

Algebra Level 1

True or false:

$1 + i + i^2 + i^3 + i^4 + \cdots$

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

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