How do you find the power #(3-5i)^4# and express the result in rectangular form?
1 Answer
Mar 23, 2017
# (3-5i)^4 = -644 +960i #
Explanation:
We can use the binomial theorem to expand the expression. (The binomial coefficient from Pascals triangle are
# (3-5i)^4 = (3)^4 + 4(3)^3(-5i) + 6(3)^2(-5i)^2+4(3)(-5i)^3+(-5i)^4 #
# " " = 81 + 108(-5i) + 54(25i^2) + 12(-125i^3)+(625i^4) #
# " " = 81 -540i + 1350(-1)-1500(-i)+625(1) #
# " " = 81 -540i - 1350+1500i+625 #
# " " = -644 +960i #
