All about Complex Conjugate

Algebra Level pending

If complex numbers \(\alpha\) and \(\beta\) satisfy \[\alpha+\overline{\beta} = 7 i^{98}+9 i^{99} + 7 i^{100},\] what is the value of \(\alpha \overline{\alpha} + \alpha\beta + \overline{\alpha\beta} + \beta \overline{\beta}?\)

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