Maths · Algebra of complex numbers
What is the value of ^{5}+(1-i)^{5} \) where
What is the value of \( (1+i)^{5}+(1-i)^{5} \) where \( i=\sqrt{-1} ? \)
- A. -8
- B. 8
- C. \( 8 i \)
- D. \( -8 i \)
Step-by-step solution
Compute (1+i)^2 = 2i, then (1+i)^4 = (2i)^2 = -4, so (1+i)^5 = (1+i)^4 * (1+i) = -4(1+i) = -4 - 4i. Its conjugate (1-i)^5 = -4 + 4i. Sum = -8.
Related MCQs
- The sequence upto 100 times simplifies to where…
- If x+(1+i) y=1-3 i, \) then = \)…
- The value of can be? This question has multiple correct options…
- Let be any complex number such that is a purely imaginary number. Then is :…
- If is a cube root of unity and ^{n}=1+12 \omega+69 \omega+\ldots . \) then values of and respectively are…