Harvard Entrance Exam Question | Can you solve?

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[DuncanMaggs]

You need to write the pi symbol more clearly as it often appears as though you are writing the variable x!

[sonicbreaker]

your answer is one of the infinitely-many values. this is because -1 = exp[i*(pi + 2*pi*n)] where n = ..., -2, -1, 0, 1, 2, ...
therefore, the final answer is exp[i*pi^3/2 (1+2*n)] where n = ..., -2, -1, 0, 1, 2, ...

[padraiggluck]

cos(π^3/2) + sin(π^3/2)*i ~= (0.7551868, -0.6555097) (together with all z that differ by 2π in the argument)

[SGuerra]

A questão é interessante, mas é preciso especificar melhor até que ponto deve- se resolvê-la. BRASIL Dezembro de 2024.

[maherhaddad]

The answer is more complicated then the equation to solve!?

[pelasgeuspelasgeus]

Euler formula is simply wrong. One side is the exp function which tends to infinity and the other side is a sum of 2 trig functions each ranging from -1 to 1, ie it's finite. So, these 2 sides can't be equal.