Complex Numbers and Their Powers

The video tutorial explains how to raise the complex number 2 + 2i to the 5th power using De Moivre's Theorem. It begins by converting the complex number into polar form and identifying the reference triangle. The tutorial then applies De Moivre's Theorem to calculate the power, using the unit circle to find trigonometric values. Finally, the result is verified using a graphing calculator, ensuring the calculation is correct.

What is the initial complex number that we are raising to the 5th power?

• 3 + 3i

• 4 + 4i

• 2 + 2i

• 1 + i

Which theorem is used to raise the complex number to a power in this example?

• Fundamental Theorem of Algebra

• Pythagorean Theorem

• De Moivre's Theorem

• Binomial Theorem

What is the angle theta for the complex number 2 + 2i on the coordinate plane?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

What is the value of R for the complex number 2 + 2i in polar form?

• 2

• 2√2

• 4

• √2

In polar form, what is the expression for Z to the 5th power?

• R^5 * (cos(5θ) + i sin(5θ))

• R^5 * (cos(θ) + i sin(θ))

• R^5 * (cos(2θ) + i sin(2θ))

• R^5 * (cos(3θ) + i sin(3θ))

What is the simplified result of 2 + 2i raised to the 5th power?

• 128

• -256

• -128

• 256

What is the cosine value at 5π/4 radians on the unit circle?

• √2/2

• -√2/2

• 1/2

• -1/2

What is the sine value at 5π/4 radians on the unit circle?

• √2/2

• 1/2

• -1/2

• -√2/2

What mode should the calculator be in to verify the complex number calculation?

• Exponential mode

• Real mode

• Complex mode

• Polar mode

What is the final complex number result of raising 2 + 2i to the 5th power?

• 128 + 128i

• -128 - 128i

• 128 - 128i

• -128 + 128i