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  "body": "\n## Statement\n\nLet $z$ be a complex number with $z \\neq 0$, let $r = |z|$ be its [[modulus|0KW2X0TFBX]] and let $\\theta = \\operatorname{Arg} z$ be its [[principal argument|0SQSQP748R]].\nThen\n$$z = r (\\cos \\theta + i \\sin \\theta) = r e^{i \\theta}.$$\n\n## Remarks\n\nThe second equality is [[Euler's formula|04R3CY41VJ]].\nThe pair $(r, \\theta)$ gives the polar coordinates of the point $z$ in the [[complex plane|0CTE7A31XQ]].\nPolar form makes products easy: $r e^{i \\theta} \\cdot s e^{i \\varphi} = r s \\, e^{i (\\theta + \\varphi)}$.\n\n## Explanations\n\n### L1 human\n\nYou can describe a point of the plane by its distance from $0$ and its direction.\nFor example, $1 + i$ has distance $\\sqrt{2}$ and direction $\\pi/4$, so $1 + i = \\sqrt{2} \\, e^{i \\pi/4}$.\n",
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    "name": "Polar form",
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