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Complex numbers/Computations/Exercise

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< Complex numbers

Calculate the following expressions in the complex numbers.

${}(5+4{\mathrm {i} })(3-2{\mathrm {i} })$ .
${}(2+3{\mathrm {i} })(2-4{\mathrm {i} })+3(1-{\mathrm {i} })$ .
${}(2{\mathrm {i} }+3)^{2}$ .
${}{\mathrm {i} }^{1011}$ .
${}(-2+5{\mathrm {i} })^{-1}$ .
${}{\frac {4-3{\mathrm {i} }}{2+{\mathrm {i} }}}$ .

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Mathematical exercise