// Numbas version: finer_feedback_settings
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Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.
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\nInput $a$ and $b$ as fractions or integers only.
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$z=\\;\\;$[[0]] + [[1]] i
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$z=\\;\\;$[[0]] + [[1]] i
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\n\nwhen \\[z=i^0\\] $z=\\;\\;$ [[0]]
\nwhen \\[z=i^1\\] $z=\\;\\;$ [[1]]
\nwhen \\[z=i^2\\] $z=\\;\\;$ [[2]]
\nwhen \\[z=i^3\\]$z=\\;\\;$ [[3]]
\nHence, or otherwise calculate
\n\\[z=i^{\\var{n}}\\]
$z=\\;\\;$[[4]]
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