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Question

Mathematics Question on Complex Numbers and Quadratic Equations

Express the given complex number in the form a+ib:i−39a + ib: i^{-39}

Answer

i−39=i−4×9−3 i^{-39}=i^{-4 × 9-3}

=(i4)−9×i−3=(i^{4})^{-9}× i^{-3}

=1i−3=1−i=\dfrac{1}{i^{-3}}=\dfrac{1}{-i}

=−1i×ii=\dfrac{-1}{i} × \dfrac{i}{i}

=i=i (Ans.)