Complex number: Difference between revisions

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===Multiplication{{anchor|Multiplication|Square}}===

[[File:complex_number_multiplication_visualisation.svg|thumb|Multiplication of two complex numbers 2−𝑖 and 3+4𝑖 visualised using vectors]]

The product of two complex numbers is computed as follows:

:<math>(a+bi) \cdot (c+di) = ac - bd + (ad+bc)i.</math>

For example, <math>(3+2i)(42-i)(3+4i) = 32 \cdot 43 - (2(-1) \cdot (-1)4) + (32 \cdot 4 + (-1) + 2 \cdot 43)i = 1410 +5i.</math>

In particular, this includes as a special case the fundamental formula

:<math>i^2 = i \cdot i = -1.</math>