Questions from General Calculus

Q: Find the indicated roots. Sketch the roots in the complex plane

Find the indicated roots. Sketch the roots in the complex plane. The cube roots of 1 + i

Q: Write the number in the form a + bi. e

Write the number in the form a + bi. e iπ/2

Q: Write the number in the form a + bi. e

Write the number in the form a + bi. e 2πi

Q: Write the number in the form a + bi. e

Write the number in the form a + bi. e iπ/3

Q: Write the number in the form a + bi. e

Write the number in the form a + bi. e -iπ

Q: Write the number in the form a + bi. e

Write the number in the form a + bi. e 2 + iπ

Q: Write the number in the form a + bi. e

Write the number in the form a + bi. e π+i

Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ

Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

Q: Use Euler’s formula to prove the following formulas for cos x and

Use Euler’s formula to prove the following formulas for cos x and sin x:

Q: Find the area of the region that lies inside the first curve

Find the area of the region that lies inside the first curve and outside the second curve.