-i squared square root of -80

To calculate the expression -i squared square root of -80, we need to break it down step by step.

1. Start with -i: This represents the complex number -1 times the imaginary unit i.

2. Square -i: When we square -i, we multiply it by itself. (-i)^2 = -1 * -1 * i * i = 1 * -1 * -1 = -1.

3. Take the square root of -80: The square root of -80 is a complex number because it involves the imaginary unit. To find it, we can use the formula:

√(a + bi) = ±(√((√(a^2 + b^2) + a) / 2) + (√(a^2 + b^2) / 2)i)

In this case, a = 0 (since we don't have a real part), and b = -80. Plugging these values into the formula, we have:

√(-80) = ±(√((√((-80)^2 + 0^2) + 0) / 2) + (√((-80)^2 + 0^2) / 2)i)
= ±(√((√(6400) + 0) / 2) + (√(6400) / 2)i)
= ±(√((80) / 2) + (80 / 2)i)
= ±(√(40) + 40i)
= ±(2√10 + 40i)

4. Multiply -1 by √(-80): Finally, we multiply -1 by √(-80):

-1 * (2√10 + 40i) = -2√10 - 40i

So, the expression -i squared square root of -80 simplifies to -2√10 - 40i.