Score
How to play
Cartesian mode. Choose six tiles one at a time from the complex pile (numbers such as with a real part and an imaginary part) and the pile of real or imaginary numbers (such as or ), or pick how many complex tiles you want. The target stays hidden until you press Start the clock (or Reveal the target with no clock): then it appears and the clock starts.
Tap a tile, an operation, then another tile to combine them. The answer becomes a new tile you can use. You don't have to use all six, and each can only be used once. A division only counts when the answer is a Gaussian integer (its real and imaginary parts are whole numbers), and no step may give 0.
The modulus : tap a tile, then |z|, to replace it by its modulus, its distance from (a real number, so the point turns onto the positive real axis). In Cartesian mode only counts when it is a whole number, such as or ; in modulus–argument form .
Modulus–argument mode. The tiles and the target are in modulus–argument form, , or exponential form, , with arguments that are multiples of , or . Only × and ÷ (and the modulus) are allowed: multiply the moduli and add the arguments, or divide the moduli and subtract the arguments, and bring the argument back into . A division only counts when the modulus stays a whole number. A number with argument 0 is just written as a real number.
Both forms. Every tile and the target have an argument that is a multiple of , so each can be written exactly as or as (for example ). Tap ⇄ on a number (or hold it down, or press F) to switch its form, or use Show all as. Adding and subtracting are easier in ; multiplying and dividing are easier in . A number made by adding or subtracting may not have such a nice argument: its exponential form then shows the argument to 3 significant figures (≈). The rules are the Cartesian ones (a division only counts when the answer is a Gaussian integer). Your working is written in the form each step was done in, with the conversion when the form changes.
Both forms, Harder: π/6 and π/3. The tiles and the target have arguments that are multiples of , so their parts have in them: , . Everything is worked out exactly, for example . A division only counts when the answer is a whole-number combination of , , and (as a Gaussian integer is a whole-number combination of 1 and ): so counts, but doesn't. The modulus counts when it is with whole numbers and (). With Show your working, type with the √ key (for example 1+√3i, or √3/2+1/2i).
How close you are is the distance between your number and the target on the Argand diagram, . The faint circles round the target have radius 1, 2 and 3.
Modulus |z| (in the options, on unless you turn it off): with it off there is no |z| button, and the targets and best solutions don't use it.
Keys: 1–9 pick a tile, + - * / the operation, | or M the modulus, Backspace undoes, Enter declares.