🔢Complex Number Calculator
A complex number z = a + bi combines real part a and imaginary part b, where i = √(−1). Complex numbers extend the real line to a 2D plane and are essential in engineering, physics, and signal processing.
- 1Addition: (a+bi)+(c+di) = (a+c)+(b+d)i
- 2Multiplication: (a+bi)(c+di) = (ac−bd)+(ad+bc)i
- 3Magnitude |z| = √(a²+b²) · Argument θ = atan2(b,a)
(3+4i) × (1−2i)=11−2i · |z|=√125(3+8)+(4-6)i=11-2i
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Fun Fact
Initially dismissed as imaginary, complex numbers are now indispensable in quantum mechanics (all wave functions are complex-valued) and signal processing (Fourier transforms).
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