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Quater-imaginary base
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===Example=== If the quater-imaginary representation of the complex unit ''i'' has to be found, the formula without radix point will not suffice. Therefore, the above formula should be used. Hence: :<math> \begin{align} i & = 32id_{5}+16d_{4}-8id_{3}-4d_{2}+2id_{1}+d_{0}+\frac{1}{2i}d_{-1}+\frac{1}{-4}d_{-2}+\frac{1}{-8i}d_{-3}\\ & = i(32d_{5}-8d_{3}+2d_{1}-\frac{1}{2}d_{-1}+\frac{1}{8}d_{-3})+16d_{4}-4d_{2}+d_{0}-\frac{1}{4}d_{-2}\\ \end{align} </math> for certain coefficients ''d<sub>k</sub>''. Then because the real part has to be zero: ''d''<sub>4</sub> = ''d''<sub>2</sub> = ''d''<sub>0</sub> = ''d''<sub>β2</sub> = 0. For the imaginary part, if ''d''<sub>5</sub> = ''d''<sub>3</sub> = ''d''<sub>β3</sub> = 0 and when ''d''<sub>1</sub> = 1 and ''d''<sub>β1</sub> = 2 the digit string can be found. Using the above coefficients in the digit string the result is: :<math>i = 10.2_{2i}.</math>
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