What are the solutions to the equation z^2 + 2z + 5 = 0?
Answer and explanation
Correct answer: D. z = -1 + 2i and z = -1 - 2i
- Step 1: Quadratic formula: z = (-2 +/- sqrt(4 - 4(1)(5))) / 2 = (-2 +/- sqrt(-16)) / 2. Step 2. sqrt(-16) = 4i. Therefore z = (-2 +/- 4i) / 2 = -1 +/- 2i. Answer: z = -1 + 2i and z = -1 - 2i. Why not the others: The roots are complex conjugates because coefficients are real.
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