I know that this is an old question, but I bought a similar calculator and had the same question. The manual that comes with the calculator is a joke and doesn't actually say how to use the a and b buttons.
The calculator that I bought is a 'Jot Scientific Calcultor' from Dollar Tree.
The relevant buttons are:
'a' (with second function '->r<theta>')
'b' (with second function '->xy')
'->' (with second function 'CPLX')
'a' and 'b' are used to enter the first and second values of a paired number, or to switch between the display for a paired number.
For example, to convert from rectangular to polar coordinates:
enter the X coordinate and press 'a' there will be no apparent change on the screen.
enter the Y coordinate and press 'b'
press '2ndF' and '->r<theta>' and the screen will blank during the calculation
the r value will be displayed. press 'b' to see the theta value.
To convert from polar to rectangular:
enter the r coordinate and press 'a'
enter the theta coordinate and press 'b'
press '2ndF' and '->xy' and the screen will blank during the calculation
the X value will be displayed. press 'b' to see the Y value.
The 'CPLX' button toggles the system into complex mode. In complex mode you use the 'a' and 'b' buttons to enter the real and imaginary components of the number, and then the +-*/ functions can be used to operate on the complex values. None of the other functions work (eg no complex exponentials)
The key sequence:
'2ndF' 'CPLX' enters complex mode
'2' 'sqrt' 'a' (puts square root of 2 into the real part of the operand)
'2' 'b' ( puts 2 into the imaginary part of the operand)
'X' (multiplication) (screen changes to 0, waiting for next operand)
'2' 'sqrt' 'b'
press 'b' displays 6
(1.4142 + 2i) * (2 + 1.4142i) = (0+ 6i)