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

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Answer 1 · 2016-07-04T07:48:55

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

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

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

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

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

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

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

$=1/(8-7i)$

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

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

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

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