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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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Express the answers to parts (a) and (b) in the form $a+bi$.

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Input $a$ and $b$ as fractions or integers only.

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\\[z=(\\var{z2})^4\\]
$z=\\;\\;$[[0]] + [[1]] i

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\\[z=(\\var{z3})^{\\var{-d1}}\\]
$z=\\;\\;$[[0]] + [[1]] i

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Make sure that you input the real and imaginary parts as fractions and not as decimals

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Use integers or letters only for part (c) answers below.

\n

\n

when  \\[z=i^0\\] $z=\\;\\;$ [[0]]

\n

when  \\[z=i^1\\] $z=\\;\\;$ [[1]]

\n

when  \\[z=i^2\\] $z=\\;\\;$ [[2]]  

\n

when  \\[z=i^3\\]$z=\\;\\;$ [[3]]

\n

Hence, or otherwise calculate

\n

\\[z=i^{\\var{n}}\\]
$z=\\;\\;$[[4]]

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