If x²+2=0 and x²=−4 give rise to complex numbers, what if the constant is an odd number

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Step 1: Consider the general form of the equation x² + C = 0. This equation can be rearranged to solve for x²: x² = −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. x² = −3 Step 3: To find x, we take the square root of both sides. x = ± √(−3); Step 4: We know that √(−1) = i (the imaginary unit). So, we can rewrite the expression: x = ± √(3) · √(−1); x = ± √(3)i These solutions are complex numbers. The parity (odd or even) of a positive constant C in an equation of the form x²+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

If x²+2=0 and x²=-4 give rise to complex numbers, what if the constant is an odd number

Answer

Step-by-step solution

Consider the general form of the equation $x^2 + C = 0$ .

If the constant $C$ is a positive odd number (like 1, 3, 5, etc.), let's use $C=3$ as an example.

To find $x$ , we take the square root of both sides.

We know that $\sqrt{-1} = i$ (the imaginary unit).

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