1f:["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M8.228 9c.549-1.165 2.03-2 3.772-2 2.21 0 4 1.343 4 3 0 1.4-1.278 2.575-3.006 2.907-.542.104-.994.54-.994 1.093m0 3h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"}] 20:["$","div",null,{"className":"flex-1","children":[["$","h1",null,{"className":"text-2xl font-bold text-gray-900 mb-4","children":["$","div",null,{"dangerouslySetInnerHTML":{"__html":"

Find the multiplicative inverse of 2 – 3i.

"}}]}],["$","div",null,{"className":"flex flex-wrap gap-2 mb-4","children":[["$","span",null,{"className":"bg-sky-100 text-sky-700 px-3 py-1 rounded-full text-sm font-medium","children":"Class 11"}],["$","span",null,{"className":"bg-green-100 text-green-700 px-3 py-1 rounded-full text-sm font-medium","children":"Mathematics"}],["$","span",null,{"className":"bg-purple-100 text-purple-700 px-3 py-1 rounded-full text-sm font-medium","children":"Complex Numbers and Quadratic Equations"}]]}]]}] 21:["$","div",null,{"className":"bg-white rounded-lg shadow-md p-6","children":[["$","div",null,{"className":"flex items-center gap-2 mb-4","children":[["$","svg",null,{"className":"w-5 h-5 text-green-600","fill":"currentColor","viewBox":"0 0 20 20","children":["$","path",null,{"fillRule":"evenodd","d":"M10 18a8 8 0 100-16 8 8 0 000 16zm3.707-9.293a1 1 0 00-1.414-1.414L9 10.586 7.707 9.293a1 1 0 00-1.414 1.414l2 2a1 1 0 001.414 0l4-4z","clipRule":"evenodd"}]}],["$","h2",null,{"className":"text-xl font-bold text-gray-900","children":"Verified Answer"}]]}],["$","div",null,{"className":"prose max-w-none","children":["$","div",null,{"dangerouslySetInnerHTML":{"__html":"

Let z = 2 - 3i

Then z̄ = 2 + 3i and |z|² = 2² + (-3)² = 13

Therefore, the multiplicative inverse of 2 - 3i is given by

z^-1 = ^z̄/_|z|² = 2 + 3i/13 = 2/13 + 3/13i

"}}]}]]}] 18:[["$","meta","0",{"charSet":"utf-8"}],["$","meta","1",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","2",{"name":"theme-color","content":"#ffffff"}]] 15:null