Mysterious Complex Numbers
A gaussian integers is a complex number , where and are integers.
How many gaussian integers satisfy ?
The answer is 841.
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1 solution
This can be solved using some logic. Since, we have absolute values, we can see that there are two choices for each component of z, positive and negative. This leads us to four overall choices, (Re(z) is positive and Im(z) is positive, Re(z) is negative and Im(z) is positive, Re(z) is negative and Im(z) is negative, and Re(z) is positive and Im(z) is negative). This means that we ould look at just one, let's say the first, and then multiply all by 4. This is because the four parts are the same apart from signage. This means that the answer must be a multiple of 4. Our only choice that satisfies this is 8 4 0 .