Final answer:
The complex equation 6 - 3j = 10j - 13j has no solutions as it simplifies to a contradiction, 6 = 0. If considered as an incomplete quadratic equation, the solutions would depend on the discriminant of the quadratic formula. Nevertheless, the correct option as per the student's question is there are no solutions. b and c is correct.
Step-by-step explanation:
The complex equation 6 − 3j = 10j − 13j is a linear equation in the variable 'j'. The first step to solve it is to combine like terms on each side (if necessary) and then isolate the variable. Since 10j − 13j simplifies to −3j, the equation becomes 6 − 3j = −3j. By adding 3j to both sides, you get 6 = 0, which is a contradiction since 6 is not equal to 0. This means there are no solutions to the original equation.
However, if we examine the reference information provided and consider that it could be an incomplete quadratic equation in standard form (ax^2 + bx + c = 0), where a = 3, b = 13, c = -10, we can use the quadratic formula to find the solutions for 'x'. Substituting values into the quadratic formula, we get x = −13 ± √(13)^2 - 4 × 3 × (−10) over 2 × 3. Simplifying further, we would find the values of 'x' that satisfy the equation, usually resulting in two solutions when the discriminant is positive, one solution when it is zero, and no real solutions when it is negative. If this were the case and the discriminant were non-negative, then the equation would have 1 or 2 solutions.