[BUG] Complex vjps are wrong for arcsin/arccos/arctan/arcsinh/arccosh/arctanh (missing conjugate) #3778

Describe the bug

The inverse trigonometric / hyperbolic ops return the wrong gradient for complex inputs: their vjp delegates to their jvp, so the conjugate is dropped. For a holomorphic f the vjp must be cotangent * conj(f'(z)).

Affected: arccos, arccosh, arcsin, arcsinh, arctan, arctanh.

This is the same issue fixed for square/sin/tanh/… in #3766.

To Reproduce

import mlx.core as mx
z = mx.array(0.3 + 0.2j, mx.complex64)
g = mx.array(1.0 + 1.0j, mx.complex64)
vjp = mx.vjp(mx.arctan, [z], [g])[1][0]
expected = g * mx.conj(1 / (1 + z**2))   # cotangent * conj(f'(z))
print(vjp, expected)   # differ

Expected behavior

vjp == cotangent * conj(f'(z)), consistent with mx.exp/mx.log and finite differences.

Desktop

• OS: macOS
• Version: main (0.32.0.dev)