Questions that ask for a structured proof of a general identity or property of complex numbers (e.g., conjugate of a product, properties of decompositions), often as 'organized presentation of knowledge'.
Show that: $$( \cos ( t ) ) ^ { 2 p } = \frac { 1 } { 2 ^ { 2 p } } \left( \binom { 2 p } { p } + 2 \sum _ { k = 0 } ^ { p - 1 } \binom { 2 p } { k } \cos ( 2 ( p - k ) t ) \right)$$ Hint: One may develop $\left( \frac { e ^ { \mathrm{i} t } + e ^ { - \mathrm{i} t } } { 2 } \right) ^ { 2 p }$.