Final answer:
To use de Moivre's Theorem, we need to raise the given complex number (√2 cis 5π/24) to the eighth power. By applying de Moivre's Theorem, we can find (√2 cis 5π/24)⁸ as 16 cis (10π/3).
Step-by-step explanation:
To use de Moivre's Theorem, we need to raise the given complex number (√2 cis 5π/24) to the eighth power. De Moivre's Theorem states that if we have a complex number in the form r cis θ, then its nth power is given by (r^n) cis (nθ). For our complex number (√2 cis 5π/24), we have r = √2 and θ = 5π/24. So, to find (√2 cis 5π/24)⁸, we raise the modulus (√2) to the eighth power and multiply it by the angle (5π/24) multiplied by 8.
Calculating (√2)⁸ gives (2⁴) = 16, and calculating (5π/24) multiplied by 8 gives 10π/3. Therefore, (√2 cis 5π/24)⁸ can be written as 16 cis (10π/3) in standard form.