# Concept derivation guides

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Concept guide



## [Complex numbers: computing (2+3i)(4−5i) as an ordered pair and deciding equality](/en/derivations/derivation-mko-complex-number-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-complex-number)

Let z=2+3i and w=4−5i. Find z+w, z−w and z·w as ordered pairs (real part, imaginary coefficient). For the product, first derive the general formula (a+bi)(c+di)=(ac−bd)+(ad+bc)i from distributivity and i²=−1, then substitute the numbers and cross-check by direct expansion; finally decide whether z·w equals the real number 23.

Complex number

derivation-mko-complex-number-01





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