lean_workbook_plus_13982

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Setting $z=a+bi$ , $z^3=(a+bi)^3=a^3+3a^2bi-3ab^2-b^3i$ \nSo $3a^2b-b^3=11$ , $a^3-3ab^2=2$ . After this, you need to find a way to solve for $a$ and $b$ . However I am not sure if this is the fastest method.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_13982 (a b : ℝ) (z : ℂ) (h₀ : z = a + b * Complex.I) (h₁ : z^3 = 11 + 2 * Complex.I) : 3 * a^2 * b - b^3 = 11 ∧ a^3 - 3 * a * b^2 = 2   :=  by sorry

The cube’s real and imaginary parts are interchanged relative to the hypothesis11+2i.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

For z=a+bi and z³=11+2i, conclude a³−3ab²=11 and3a²b−b³=2. If source intended2+11i, change the complex hypothesis instead.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.