Nice Math Olympiad Algebra Problem | Fully Solved.

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• Japanese | Can you sol...

[@ayb109]

Simpler method is factoring the left side first:
sqrt(y)(1 ± i) = 4
Then square, (1 ± i)^2 = ±2i so:
±2iy = 16
y = ±8i

[@mrhaki1962]

Effectivement c'est à quoi j'ai pensé dès le premier coup d'œil

[@MasterTMathsClass]

Nice

[@roland3et]

sqrt(y) + sqrt(-y) = 4
Why this confusing and incredibly complicated number juggling back and forth?
Just square the original equation at the very beginning, and you get the solution almost right away:
(sqrt(y) + sqrt(-y))² = 4²
y + 2sqrt(y)sqrt(-y) - y = 16
sqrt(y)sqrt(-y) = 8 | square
y(-y) = -y² = 64
y² = -64
y = ±sqrt(-64) = ±8i (with i²=-1)
That's it.
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