De Moivre’s and the nth Root Theorems
Topic Page
De Moivre’s and the nth Root TheoremsQuestions
- How do you use De Moivre’s Theorem to find the powers of complex numbers in polar form?
- What is the DeMoivre's theorem used for?
- How do you find the #n^{th}# roots of complex numbers in polar form?
- How do you find #[2(\cos 120^\circ + i \sin 120^\circ)]^5# using the De Moivre's theorem?
- What is #(-\frac{1}{2}+\frac{i\sqrt{3}}{2})^{10}#?
- How do you find the three cube roots of #-2-2i \sqrt{3}#?
- If the roots can be determined, will some form of De Moivre’s Theorem be used?
- How do you find the two square roots of 2i?
- Question #f6317
- How do you find #z, z^2, z^3, z^4# given #z=sqrt2/2(1+i)#?
- How do you find #z, z^2, z^3, z^4# given #z=1/2(1+sqrt3i)#?
- How do you use DeMoivre's Theorem to simplify #(2+i)^5#?
- How do you use DeMoivre's Theorem to simplify #(2+2i)^6#?
- How do you use DeMoivre's Theorem to simplify #(3-2i)^8#?
- How do you use DeMoivre's Theorem to simplify #2(sqrt3+i)^7#?
- How do you use DeMoivre's Theorem to simplify #(5(cos20+isin20))^3#?
- How do you use DeMoivre's Theorem to simplify #(cos0+isin0)^20#?
- How do you use DeMoivre's Theorem to simplify #(cos(pi/4)+isin(pi/4))^12#?
- How do you use DeMoivre's Theorem to simplify #(2(cos(pi/2)+isin(pi/2)))^8#?
- How do you use DeMoivre's Theorem to simplify #(5(cos3.2+isin3.2))^4#?
- How do you use DeMoivre's Theorem to simplify #(3-2i)^5#?
- How do you use DeMoivre's Theorem to simplify #(sqrt5-4i)^3#?
- How do you use DeMoivre's Theorem to simplify #(3(cos15+isin15))^4#?
- How do you use DeMoivre's Theorem to simplify #(2(cos10+isin10))^8#?
- How do you use DeMoivre's Theorem to simplify #(2(cos(pi/10)+isin(pi/10)))^5#?
- How do you use DeMoivre's Theorem to simplify #(2(cos(pi/8)+isin(pi/8)))^6#?
- How do you find the cube roots of #8(cos((2pi)/3)+isin((2pi)/3))#?
- How do you find the square roots of #-25i#?
- How do you find the fourth roots of #625i#?
- How do you find the fourth roots of #16#?
- How do you find the cube roots of #1000#?
- How do you find the cube roots of #-125#?
- How do you find the fourth roots of #-4#?
- How do you find the fifth roots of #128(-1+i)#?
- How do you find the sixth roots of #64i#?
- How do you use DeMoivre's theorem to simplify #(1+i)^4#?
- How do you use DeMoivre's theorem to simplify #(2+2i)^6#?
- How do you use DeMoivre's theorem to simplify #(sqrt3+i)^7#?
- How do you use DeMoivre's theorem to simplify #(1-sqrt3i)^3#?
- How do you use DeMoivre's theorem to simplify #(5(cos(pi/9)+isin(pi/9)))^3#?
- How do you use DeMoivre's theorem to simplify #(3(cos((5pi)/6)+isin((5pi)/6)))^4#?
- How do you use DeMoivre's theorem to simplify #(2e^(30i))^3#?
- How do you use DeMoivre's theorem to simplify #(5e^(15i))^3#?
- How do you use DeMoivre's theorem to simplify #(sqrt(e^(10i)))^6#?
- How do you use DeMoivre's theorem to simplify #(sqrt2e^(15i))^8#?
- How do you use DeMoivre's theorem to simplify #(1+isqrt3)^3#?
- How do you use DeMoivre's theorem to simplify #(sqrt3+i)^8#?
- How do you use DeMoivre's theorem to simplify #(-sqrt3-i)^4#?
- How do you use DeMoivre's theorem to simplify #(-1+i)^4#?
- How do you use DeMoivre's theorem to simplify #(-sqrt3+i)^5#?
- How do you use DeMoivre's theorem to simplify #(-1/2+sqrt3/2i)^3#?
- How do you use DeMoivre's theorem to simplify #(-1/2-sqrt3/2i)^3#?
- How do you find the 3rd root of #8e^(30i)#?
- How do you find the 3rd root of #8e^(45i)#?
- How do you find the 4rd root of #81e^(60i)#?
- How do you find the 4rd root of #16e^(90i)#?
- How do you find the 5th root of #1-i#?
- How do you find the 3rd root of #-1+i#?
- Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. (Round terms to four decimal places.)?
- Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form?
- Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form?
- Using De Moivre's Theorem, What is the indicated power of #(-sqrt2 -sqrt2 i)^5#?
- How do you use De Moivre's Theorem to simplify #z=(2[cos(5pi/4)+isin(5pi/4)])^5# to #16sqrt2 + 16sqrt2 i#?
- How do you verify that De Moivre's Theorem holds for the power n=0?