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设Z_1、Z_2是不为零的复数,则||Z_1|-|Z_2||≤|Z_1±Z_2|≤|Z_1|+|Z_1|．(1)我们把(1)式叫做复数的三角不等式,等号当且仅当复数Z_1、Z_2的对应向量OZ_1、OZ_2同向时成立．其几何意义为“三角形的两边之和大于第三边．两边之差小于第三边．”根据复数模的性质和绝对值不等式的性质还可以推广如下：设Z_1、Z_2、Z_3是不为零的复数,
Let Z_1, Z_2 be a complex number that is not zero, then ||Z_1|-|Z_2|| ≤|Z_1±Z_2| ≤|Z_1|+|Z_1|. (1) We call (1) the complex triangle inequality, and the equal sign holds if and only if the corresponding vectors OZ_1 and OZ_2 of the complex numbers Z_1 and Z_2 are in the same direction. The geometric meaning is “the sum of the sides of the triangle is greater than the third side. The difference between the two sides is smaller than the third side.” Depending on the properties of the complex modulus and the nature of the absolute value inequality, it can also be generalized as follows: Let Z_1, Z_2, Z_3 be non-zero The plural,