SUMMARY
The discussion centers around verifying the equation (1+i)^(95) = (1-i)*2^(47). The user initially miscalculated the expression, mistakenly arriving at (1+i)*2^(47) instead. The correct approach involves using the polar form of complex numbers, specifically z^(n) = r^(n) * e^(i*n*theta), and accurately determining the sine value for theta. The user corrected their error regarding sin(95π/4), realizing it should be -1/√2 instead of 1/√2.
PREREQUISITES
- Understanding of complex numbers and their polar representation
- Familiarity with De Moivre's Theorem
- Knowledge of trigonometric functions, particularly sine and cosine
- Experience with exponentiation of complex numbers
NEXT STEPS
- Study De Moivre's Theorem in detail
- Learn about the polar form of complex numbers
- Practice calculating powers of complex numbers using trigonometric identities
- Explore advanced topics in complex analysis, such as Euler's formula
USEFUL FOR
Mathematics students, educators, and anyone interested in complex number theory and its applications in solving equations.
