complex(7)

💖 complex(7) — Miscellaneous Information Manual 💖

okay bestie, pull up a chair, because we're doing complex(7) from the miscellaneous info section and it's literally the glow-up era of math 🌈✨

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✨ NAME ✨

complex — the basics of complex mathematics, and yes she's iconic for it 👑

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🎀 LIBRARY 🎀

Math library (libm, -lm) — go link her, she's waiting 🫶

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🌸 SYNOPSIS 🌸

#include <complex.h>

that's it, that's the whole vibe check 💅

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💜 DESCRIPTION 💜

So. Complex numbers, right? They're numbers shaped like z = a+b*i, where a and b are real numbers and i = sqrt(-1), which means i*i = -1. no cap, that's literally the whole definition and she ate 🔥

There's more than one way to represent that same number, bestie. You can take the pair (a,b) of real numbers and read it as a point in the plane — the X- and Y-coordinates, super chill, very "graph it and go". ✨ But wait ✨ — that exact same point can also be described by a different pair of real numbers, (r,phi), where r is the distance to the origin O, and phi is the angle between the X-axis and the line Oz. And then:

z = r*exp(i*phi) = r*(cos(phi)+i*sin(phi))

two representations, one queen 🧚

The basic operations, defined on z = a+b*i and w = c+d*i, are:

• addition: z+w = (a+c) + (b+d)*i
• multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i
• division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i

not me memorizing the division one, it's giving "plot twist at the denominator" 😭

And here's the tea: nearly all math function have a complex counterpart — but there are some complex-only functions. those ones are special, iykyk 💅

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🌟 EXAMPLES 🌟

Your C-compiler can work with complex numbers if it supports the C99 standard. The imaginary unit is represented by I. uppercase, diva behavior, respect it 💅

/* check that exp(i * pi) == -1 */
#include <math.h>        /* for atan */
#include <stdio.h>
#include <complex.h>

int
main(void)
{
    double pi = 4 * atan(1.0);
    double complex z = cexp(I * pi);
    printf("%f + %f * i\n", creal(z), cimag(z));
}

it prints and everything, main character energy fr fr 🎀

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🦋 SEE ALSO 🦋

the whole friend group, no one left out 💖

• cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3), catanh(3), ccos(3), ccosh(3), cerf(3), cexp(3), cexp2(3), cimag(3), clog(3), clog10(3), clog2(3), conj(3), cpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)

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and that's the page, bestie!! 💜 this one's from Linux man-pages 6.20, dated 2026-02-08 — so like, remember the date for the exam or whatever 🙈 slay, go write some #include <complex.h> code, mwah 💅✨🌸