(a)[5]
Show all working, and solve the equation $iz^2 + 2z - 3i = 0$, writing your answers in the form $x + iy$, where $x$ and $y$ are exact real numbers.
(b(i))[2]
On an Argand diagram sketch, draw the locus of complex numbers that satisfy $|z| = |z - 4 - 3i|$.
(b(ii))[3]
Determine the complex number shown by the point on the locus for which $|z|$ is smallest. Find its modulus and argument, and give the argument to 2 decimal places.