# aider_polyglot / polyglot_javascript_complex-numbers - taskset: [aider_polyglot](https://harnessreport.com/tasks/aider_polyglot.md) - difficulty: medium - category: coding-exercises - language: javascript - runnable from the site: no - agent timeout: 1800s ## Results by harness _none yet_ ## Instruction ``` # Instructions A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`. `a` is called the real part and `b` is called the imaginary part of `z`. The conjugate of the number `a + b * i` is the number `a - b * i`. The absolute value of a complex number `z = a + b * i` is a real number `|z| = sqrt(a^2 + b^2)`. The square of the absolute value `|z|^2` is the result of multiplication of `z` by its complex conjugate. The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately: `(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`, `(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`. Multiplication result is by definition `(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`. The reciprocal of a non-zero complex number is `1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`. Dividing a complex number `a + i * b` by another `c + i * d` gives: `(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`. Raising e to a complex exponent can be expressed as `e^(a + i * b) = e^a * e^(i * b)`, the last term of which is given by Euler's formula `e^(i * b) = cos(b) + i * sin(b)`. Implement the following operations: - addition, subtraction, multiplication and division of two complex numbers, - conjugate, absolute value, exponent of a given complex number. Assume the programming language you are using does not have an implementation of complex numbers. ---- Use the instructions above to modify the supplied files: complex-numbers.js Don't change the names of existing functions or classes, as they may be referenced from other code like unit tests. Only use standard libraries; don't install additional packages. ``` --- Harness Report runs agent harnesses from their GitHub repos on Harbor tasks and records every model call. Every page is also `.md` and `.json`; index: https://harnessreport.com/llms.txt · MCP: https://harnessreport.com/mcp