Powers of Imaginary Numbers
Read this topicExplanations 3
- Powers of Imaginary and Complex Numbers You can perform any mathematical operation with imaginary and complex numbers! Just like we can add, subtract, multiply, and divide these…
By Jonathan Heller, Victor Wang, Caroline K, Anusha Rahman
- (Video) Complex Numbers - Powers of i | Don't Memorise by Don't Memorise In this video by Don't Memorise, we can see the derivations of i2=−1i^2 = -1i2=−1, i3=−ii^3 = -ii3=−i, a…
By Trisha, Anusha Rahman
- Powers of Imaginary Numbers Powers of imaginary numbers follow a pattern that repeats every four powers. Imaginary numbers are defined using square roots of negative real number…
By Trisha, Anusha Rahman
Problems 16
- What is 4i4i4i4i4i4?4i^{4i^{4i^{4i^{4i^4}}}}?4i4i4i4i4i4?
- What is i−1i^{-1}i−1?
- Which of these is equivalent to i1801i^{1801}i1801?
- Which of the following are equivalent to i2026?i^{2026}?i2026?
- What is (14i)2(14i)^2(14i)2?
- Evaluate this expression: 4i+6i2−2i5−8i44i + 6i^2 - 2i^5 - 8i^44i+6i2−2i5−8i4
- What is i2048i^{2048}i2048?
- What is i1729i^{1729}i1729?
- What is i442i^{4^{42}}i442?
- What is i+i2+i3+i4i+i^2+i^3+i^4i+i2+i3+i4?
- What is i−i3+i5−i7+⋯+i97−i99i-i^3+i^5-i^7+ \cdots + i^{97}-i^{99}i−i3+i5−i7+⋯+i97−i99?
- What is ii8+41i^{i^{8}+{41}}ii8+41?
- Which of these complex numbers is purely imaginary?
- What is the imaginary part of i1⋅i3⋅i5⋅i7⋅i9i^1\cdot i^3 \cdot i^5 \cdot i^7 \cdot i^9i1⋅i3⋅i5⋅i7⋅i9?
- What is (1+i)4(1+i)^4(1+i)4?
- What is the area of the polygon in the complex plane with vertices at 1,i,i2,i31,i,i^2,i^31,i,i2,i3?