What is complex conjugate of [ (3 + 8i)^4 ] / [ (1+i)^10 ](3+8i)4(1+i)10?
1 Answer
Jan 10, 2016
Explanation:
First note that
So
(1+i)^10 = (2i)^5 = (2i)^2(2i)^2(2i) = (-4)(-4)(2i) = 32i(1+i)10=(2i)5=(2i)2(2i)2(2i)=(−4)(−4)(2i)=32i
(3+8i)^4 = (9+48i+64i^2)^2 = (-55+48i)^2(3+8i)4=(9+48i+64i2)2=(−55+48i)2
= (3025-5280i+2304i^2) = 721-5280i=(3025−5280i+2304i2)=721−5280i
So:
(3+8i)^4/(1+i)^10 = (721-5280i)/(32i) = -721/32i-5280/32 = -721/32i-165 = -165-721/32i(3+8i)4(1+i)10=721−5280i32i=−72132i−528032=−72132i−165=−165−72132i
So, reversing the sign of the coefficient of
-165+721/32i−165+72132i