Past exam of the mathematical methods I course of the University of Oxford / 2021 resit / 2 / i / Solution

Multiply numerator and denominator by the denominator's complex conjugate:

\frac{3 + 2 i}{2 - 3 i} = \frac{( 3 + 2 i ) ( 2 + 3 i )}{2 ^{2} + 3 ^{2}} = \frac{6 + 13 i - 6}{13} = i .

Thus the real part and imaginary part are

Re = 0, Im = 1.

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