Question

Find all complex number solutions to the equation. 3 x-1000=0 Choose the correct solution set below. O A. (5(cos 60° + i sin 60°),5( cos 180° +isin 180°),5( cos 300° + i sin 300°)} O B. (5(cos 0° + i sin 0°),5( cos 120° + i sin 120°),5( cos 240° + i sin 240°)} OC. {10(cos 60° + i sin 60°), 10( cos 180° +isin 180°),10( cos 300° + i sin 300°)} OD. (10(cos 0° + i sin 0°), 10( cos 120° + i sin 120°), 10( cos 240° + i sin 240°)}

Answer 1

The solution to the equation 3x - 1000 = 0 is x = 333.33 in decimal form. This is a real number, so it doesn't have complex number solutions. Thus, none of the provided complex number options are correct.

Step-by-step explanation:

The given equation is 3x - 1000 = 0. This is a simple linear equation where we only need to isolate x. The first step is to add 1000 to both sides of the equation so that it becomes 3x = 1000. Then, to solve for x, we divide both sides of the equation by 3 which yields x = 1000 / 3 which simplifies to x = 333.33 (rounded to two decimal places). This is a simple real number solution. It does not have any complex number solutions.

Therefore, none of the provided options A, B, C, or D are correct because those represent complex numbers in the form of polar form and our solution does not involve complex numbers.

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