Final answer:
To remove the exponent from equation 4 = -t^2 - 3, add 3 to both sides, then take the square root of both sides, introducing the imaginary unit i due to the negative sign. This gives t = -i√(7).
Step-by-step explanation:
To remove an exponent from the equation 4 = -t^2 - 3, you first need to isolate the term with the exponent. Start by adding 3 to both sides of the equation:
4 + 3 = -t^2
7 = -t^2
Now, to proceed with getting rid of the exponent, you need to take the square root of both sides. In this situation, as you are dealing with a negative term, it's noteworthy that taking the square root of a negative number results in an imaginary number. Hence, you'll get:
√(7) = √t^2
Since √(-t^2) involves a negative under the square root, we will introduce the imaginary unit, i, resulting in:
√(7) = i√t^2
Since t^2 squared is simply |t|, the modulus of t, the equation simplifies to:
√(7) = it
Finally, to solve for t, we can multiply both sides by i to get:
t = -i√(7)
Remember that when dealing with square roots of negative numbers, the result will always involve the imaginary unit i.