Complex addition and multiplication (integral)

Complex Numbers

An integral complex number is a number of the form $a+i\cdot b$ where the real part

and the imaginary part

are both integers. Addition and multiplication of integral complex numbers results in an integral complex number.

In the following applets, the numbers

and

can be moved to integral grid points.

Please enable Java for an interactive construction (with Cinderella).

Complex Addition follows the rule

$(a_1+ib_1)+(a_2+ib_2)=(a_1+a_2)+i(b_1+b_2).$

Please enable Java for an interactive construction (with Cinderella).

Complex Multiplication follows the rule

$(a_1+ib_1)(a_2+ib_2)=(a_1b_1-a_2b_2)+i(a_1b_2+a_2b_1).$

Both operation can be easily deduced by interpreting

as a unit (of measure), simplyfying the equation as usual, but taking the special rule

into account.

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