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

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Answer 1 · 2016-07-04T07:48:55

$= \frac{1}{113} (8 + 7 i)$ $=1/113(8+7i)$

$\frac{{(7 + 8 i)}^{10}}{{(- 8 + 7 i)}^{11}}$ $(7+8i)^10/(-8+7i)^11$

$= \frac{{(7 + 8 i)}^{10}}{{(i^{2} \cdot 8 + 7 i)}^{11}}$ $=(7+8i)^10/(i^2*8+7i)^11$

$= \frac{{(7 + 8 i)}^{10}}{i^{11} {(7 + 8 i)}^{11}}$ $=(7+8i)^10/(i^11(7+8i)^11)$

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

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

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

$=1/(8-7i)$

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

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

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

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