Rewriting H(jw) in exponential form

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Why can H(jw) be expressed as the absolute value of H(jw) multiplied by an exponent? And what is the meaning behind the actual power (j*theta(jw))?

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For any complex number $z$ one can rewrite it in polar form $z = |z|e^{i \arg(z)}$ which is presumably what they did here.