{"status": "success", "data": {"description_md": "**POTD March 4, 2024**\n\nThree complex numbers $u,v,w$ are chosen randomly so that $u \\overline{v}$ and $v \\overline{w}$ have real parts $\\frac{1}{7}$. Find the reciprocal of the expected value of the real part of $w \\overline{u}$.", "description_html": "<p><strong>POTD March 4, 2024</strong></p>&#10;<p>Three complex numbers <span class=\"katex--inline\">u,v,w</span> are chosen randomly so that <span class=\"katex--inline\">u \\overline{v}</span> and <span class=\"katex--inline\">v \\overline{w}</span> have real parts <span class=\"katex--inline\">\\frac{1}{7}</span>. Find the reciprocal of the expected value of the real part of <span class=\"katex--inline\">w \\overline{u}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #86", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}