Composing multiplication by this number with the exponential function gives a function that is equal
Composing multiplication by this number with the exponential function gives a function that is equal to the negative of its second derivative. Multiples of this number plus one-half give all non- trivial zeros of the zeta function via the Riemann hypothesis. It forms a basis for the (*) quaternions alongside one and two similar numbers with which it anti-commutes. The first non-trivial fourth root of unity, this number has magnitude 1 and polar angle 90 degrees in the complex plane. For 10 points, identify this complex number, the square root of negative one.
Composing multiplication by this number with the exponential function gives a function that is equal to the negative of its second derivative.
{i} [or the imaginary number; prompt on square-root of negative one]