How do you simplify #[(7+8i)^10 / (-8+7i)^11]#?

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Answer 1 · 2016-07-04T07:48:55

#=1/113(8+7i)#

#(7+8i)^10/(-8+7i)^11#

#=(7+8i)^10/(i^2*8+7i)^11#

#=(7+8i)^10/(i^11(7+8i)^11)#

#=cancel((7+8i)^10)/(i*(i^2)^5(7+8i)cancel((7+8i)^10))#

#=1/(i*(-1)^5(7+8i))#

#=1/(-i(7+8i))=1/(-7i-8i^2)#

#=1/(8-7i)#

#=(8+7i)/((8-7i)(8+7i))#

#=(8+7i)/(8^2-7^2i^2)#

#=1/113(8+7i)#