Add √^-31+ √^−31

Answer 1

Adding √^-31 + √^-31 is equivalent to adding two complex numbers.

Let's represent √^-31 as √31i^-1, where i is the imaginary unit.

So, √^-31 + √^-31 = √31i^-1 + √31i^-1.

To simplify this expression, we can multiply both terms by i/i to eliminate the negative exponent:

√31i^-1 + √31i^-1 = (√31i^-1)(i/i) + (√31i^-1)(i/i).

Using the property i^2 = -1, we have:

(√31i^-1)(i/i) + (√31i^-1)(i/i) = (√31i^2)/(i^2) + (√31i^2)/(i^2).

Simplifying further:

(√31i^2)/(i^2) + (√31i^2)/(i^2) = (√31(-1))/(-1) + (√31(-1))/(-1).

Finally, combining like terms and simplifying:

(√31(-1))/(-1) + (√31(-1))/(-1) = -√31 - √31 = -2√31.

Therefore, √^-31 + √^-31 = -2√31.