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→Generalizations and related notions: whoops, fix align |
→Relations and operations: ce to make both subsections more direct, and they could probably be gotten rid of all together. Also, cleared up the example with equality which essentially said the same thing twice in the same way so that it actually phrased it two different ways |
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==Relations and operations==
<math>\operatorname{Re}(z_{1}) = \operatorname{Re}(z_{2})</math> and <math>\operatorname{Im} (z_{1}) = \operatorname{Im} (z_{2})</math>. Nonzero complex numbers written in [[polar form]] are equal if and only if they have the same magnitude and their arguments differ by an integer multiple of {{math|2{{pi}}}}.▼
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▲Complex numbers have a similar definition of equality to real numbers; two complex numbers <math>
Since complex numbers are naturally thought of as existing on a two-dimensional plane, there is no natural [[linear ordering]] on the set of complex numbers. In fact, there is no [[linear ordering]] on the complex numbers that is compatible with addition and multiplication – the complex numbers cannot have the structure of an [[ordered field]]. This is because any square in an ordered field is at least {{math|0}}, but {{math|1=''i''<sup>2</sup> = −1}}.▼
====ordering====
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===Conjugate===
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