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ComplexExpand

Usage

ComplexExpand[expr] 假设所有的变量都是实数来展开expr.
ComplexExpand[expr,   ,  , ...  ] 假设匹配任何 的变量都是复数来展开expr.


Notes

• 例如: ComplexExpand[Sin[x + I y]]LongRightArrow .
• 在ComplexExpand的第二个参数中给出的变量可以是模式。
• 例如: ComplexExpand[Sin[x], x]LongRightArrow .
• 可以从集合{Re, Im, Abs, Arg, Conjugate, Sign}. ComplexExpand 中的函数列表给出的选项TargetFunctions总是根据指定的函数给出结果。
ComplexExpand[expr, vars, TargetFunctions ->  Abs, Arg ] 转换为极坐标。
• 参见Mathematica全书: 1.4.5 and 节 3.3.8.
Further Examples

You can expand complex powers.

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The result here is not x  y because x or y could be complex.

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This assumes x and y are real.

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You can expand complex exponential, trig, and hyperbolic functions.

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You can expand trig and hyperbolic functions of complex arguments.

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Using the TargetFunction option

This forces Mathematica to assume both x and y are real.

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This is an expansion in terms of z and the absolute value of z.

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Now we expand in terms of polar coordinates.

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Finally, here is an expansion in terms of z and its conjugate.

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