Na disputa entre Cardano e Tartaglia pela resolução da equação polinomial do terceiro grau (século XVI), foi que se percebeu que os números reais eram insuficientes para o tratamento de equações algébricas. Em busca das raízes da equação x
3 - 15x - 4 = 0, a fórmula de Tartaglia fornecia a solução
![Imagem associada para resolução da questão](data:image/png;base64,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)
, que evidenciou a necessidade da criação do conjunto dos números complexos (÷). Em 1572, Rafael Bombelli fez a suposição de que
![Imagem associada para resolução da questão](data:image/png;base64,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)
era um número conhecido e concluiu que
![Imagem associada para resolução da questão](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIUAAAAfCAYAAADJJw4ZAAAHgElEQVR4Ae1ZaUhVXxC3tH2V6EO0QAuJKZFfkqAiiyLaPrTj8iFSySjNVsoilagvFX2IyjYi2qkkSgrLUgsytKIF2rNNtDJbaN/mz29gzv/c9+593vt82hPuwOOeZWbOnDm/M2fOeSHkkusBDw+EeNTdqusBckHhgsDLAy4ovFziNrigcDHg5QEXFF4ucRtcULgY8PKACwovl7gNQQeKgoIC2rVrF509e9avX21tbbNf1bdv39KmTZv8mr+/fjt//rzyW9CBIiQkhBryKywsVJND4c2bNxQeHs46Fy1aRH/+/DH0B2Nl5syZDfKBv/4TX9QLiu/fv9OzZ8+Ev1G/t27dYmfk5+fTly9fHP/u3LlDX79+NdjYu3dvg4MvXrxo6A/GChY1Ojra8fz98ZnI6H7zCYpjx46xQ7du3UqHDh2iKVOm0Pjx42nHjh308+fPgPtz/vz5PN6PHz9s6S4vL6dJkyaxPRDYsmULy1+5coXlv337RidPnqTbt29TTEwM91VVVdnSbcb0+PFjmjt3Lo0aNYoWLFhAjx49MmNrUNurV6/YzgsXLtjSU1dXR2vWrKG4uDgD/759+9g3EyZMoD179tCvX78M/efOnaMxY8bwEWXoILJ+0dywYQMb16lTJ1q7di2XgeAWLVpQ27Ztafjw4QEPxdCPUF8f4dzs0KGDsgkLBHrx4oVqu3z5slKjh9NTp06pdieFJ0+eKN2ir2vXrtQQkJmNv2rVKh7HcxE9eTHXzMxMg03Cs3r1atUu6zVu3DjeyAcOHFB9mMfOnTtFTH1NI8XVq1dZsHv37vT7928uY7GOHj1KSUlJ1K5dO16UsrIypaihBTgXRgLhvuj169dUWlpK2ElDhgxhGQEF5D58+MBt0IWEDYS8YsmSJdyOne4PzZ49m+U3b95Mu3fv5o0RGhpK69ev96nu79+/Pvs9O2F369atPZsNdeRF8D38ABBhPcLCwhQPdPTt25cQ6WfMmMH97du3J+RbkEGU6NKlC8F+26BISEhgB5w4cYIHmj59Oj19+lQN2q1bNzbcV4hbunQp61BC9RTgbEwG4dAupaSksIwOCsjOmzeP2xHhcnNzadq0aZSdnc1tBw8etKvewLdixQoDYOFs2JucnGzg0yvI6MFz7do1vdmy/O7dO+bH7csu3bt3zwsUEydOpJqaGlYBUHbs2JHXS9/EQ4cOpZYtW9oDBRJLoAqTwfnmSUhM0IcfdqUVLVy4kHms+tGOM1pIdErdztcKFBLp5NYhupG8mZH0e37NeKUNGwX8viKbHVA8ePBAVNL27dtZJ8Bhl8xAocu+f/+edcJW5FhCjkCBJK1z586sCEeHJ+FahwGQ1JmRRBndwchB7t+/b2BHgjh69Ghu+/z5M+vEbgZdunRJTUTXk5WVZdBhBQqctwA2dsjNmzfp+fPn9OnTJ4OsXsHRgORR/82aNUtnMZSRYMIu3GzMjgfsdN1uKR8+fNigB3ah7+PHj9zeqlUrrgvT4MGDvfQA6Pri1geKOXPmsI69e/eKWv46AkVFRQWfNzDW805/+vRpHmDQoEGGAfQKFkomBx0473r27GnI1GUHoR9OPX78OOutrKxkVUgScURBVn44Z9etW6cPRVagwBEEfpybesg0CGsVJGGRkZGG39ixYzWO/4t4HIPd+AF8ZrR//34VbYUXAJXjGDKSq6H/zJkzfP1Eefny5UrliBEjqE2bNsoH8MWAAQMI0VzIFyiOHDnCdg4bNkzY1dcRKBDOMAEYqIMC1zqZIJJCOB5XQivydXyUlJQoXdjJSIqg2ylZgQLXZWTdAEVxcXG9anUQyxz1xE0U4C4v/UVFRQxo2G8VhQT8ZjmF5A/Ql56ezoBB+e7duzKcra8VKDCm2IpEG2C+fv260ukIFLLLkJlWV1ezEh0QSNpSU1N5wD59+qhBPAuS7Xu2S13eQJAIwvj4+Hjpsv21AgXsxZUVuwy3lUAQQrY4OTY2ln3Qr18/bvMHFHiLkfO+R48eHKWg3ymZgUIHBF5HZb3wViPkCBQQwnkPA/EeoF/xxCnyRZi0IsiZJarCr4dh6MOx5YQyMjLUIkF+2bJlSnzjxo2cWffv31+1NbQQERFhGE98MHXqVEvVCPM4Ynw9xsmjGvRNnjzZUpdZh774kEd0e/jwoamd6MdLMQi5nNiPb15enkG9KTRv3LjBQpgwkkDcZc1+esJj0Gqz0qtXL2WcTRHFhj/OkPRiQgAI7t5CyHkwWeQqgSKcz2Y+0K/q/oyVk5OjfKDPwY6uly9f8jsFXpxXrlzJj4yI7mZ2IvmVBzG8cCJC4xkgLS3NKw0wBQUMGjlyJBu7bds2pcyOoU54Fi9ezGMMHDjQiZglL5JWyWUSExMt+YKpA0m17Fo9gfyXNlqCAiEvKipKAaMxjMTjFxyCYyoQJPd8XIvNroqBGCPQOuBn+ADX22AhS1CIgTij8O9lYxB2BpIgX2euk3HxaKU/iDmR/Ze8eJ/BTSVYqF5QBIuhrh1N5wEXFE3n62YzkguKZrNUTWeoC4qm83WzGckFRbNZqqYz1AVF0/m62Yz0H4Nbg3lcV/iYAAAAAElFTkSuQmCC)
e que
![Imagem associada para resolução da questão](data:image/png;base64,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)
Leonhard Euler (1707-1783) introduziu a notação i para
![Imagem associada para resolução da questão](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAcCAYAAACUJBTQAAABwklEQVRIDe1WvYrCQBCOYqO9j2BhZSM+gJ2FSDrLvIJgIdbai2KhgrZq5RukiFr40ys+gaCFCAn4N8fMcXvrJZvdnG0Wlp2dne/7MpPMEg0kYzKZgKZpsNlsJJHiY0189H1yuVxgOp3C6/WShQrPpSJCZICDUCRAsQDCcoXl8q7A8/mkawWvln9Pb+pfr2VZRF6pVKDT6QSevV5P/gnruk4imJHKcBwHxuMx7HY7Fi7tEyxROp1mAJFxPp+hWCyykvb7fRbqK7Lf7wk0m80YwMs4HA5Qr9chn89TfCwWA2WRWq1GINu2vbg9fblcDqLRqL/I/X5nYCwVPlWQIRUZDocwGAyI83Q6URbdbpf2q9UKWq2Wa67X67dn8BXZbrdEmslkCIRimMnxeKR9o9Gg/d9eaTab6iKGYTCSx+MBiUSC9j8Mt9sNrtera6KfH76Z4Lsol8tEbJomrdVqlccr2b4iyICfKpYjm83SyjeUikK73SYccsTjcVgulwR76xP8M+FrrkLMx5RKJcInk0laR6ORWwQ9qVSKAgqFAo//yH7LBJmwczGbxWLxETEPdonM53OIRCKgeiHyZCLbJSIK/MT/Bf0FxD9cOCmlAAAAAElFTkSuQmCC)
e passou a estudar os números complexos da forma z = a + ib, em que a e b são números reais e i
2 = -1.
Tendo o texto anterior como referência inicial bem como fatos históricos da matemática e a teoria dos números complexos, julgue o item que se segue.
A equação z
2 + 1 = 0 possui uma única raiz complexa.