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Complex numbers add like two-dimensional vectors: real parts together and imaginary parts together. Geometrically that is the parallelogram rule in the Argand plane.
Complex addition
(a + bi) + (c + di) = (a + c) + (b + d)i
4 − 3i, of modulus 5 and argument −36.8698976°.
Because the real and imaginary axes are independent, exactly like the x and y components of a vector.