This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Abba, good to see you again. Step 1: Consider the general form of the equation x^2 + C = 0. This equation can be rearranged to solve for x^2: x^2 = -C Step 2: If the constant C is a positive odd number (like 1, 3, 5, etc.), let's use C=3 as an example. x^2 = -3 Step 3: To find x, we take the square root of both sides. x = ± sqrt(-3) Step 4: We know that sqrt(-1) = i (the imaginary unit). So, we can rewrite the expression: x = ± sqrt(3) · sqrt(-1) x = ± sqrt(3)i These solutions are complex numbers. The parity (odd or even) of a positive constant C in an equation of the form x^2+C=0 does not change the nature of the solutions. As long as C is positive, -C will be negative, and taking the square root of a negative number will always result in complex numbers. The solutions will still be complex numbers. Complex numbers Send me the next one 📸