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Question

Answer

$\frac{20 ( 26 i + 1 ) ^{2}}{26 i (( 26 i ) ^{2} + 2 \cdot 26 i + 100 )} = \frac{1287 - 97876 i}{108706}$

Explanation

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$\frac{20 ( 26 i + 1 ) ^{2}}{26 i (( 26 i ) ^{2} + 2 \cdot 26 i + 100 )} \overset{◯}{1} \overset{◯}{2} \overset{◯}{3} \frac{20 ( 676 i ^{2} + 52 i + 1 )}{26 i ( 676 i ^{2} + 52 i + 100 )} \overset{◯}{4} \overset{◯}{5} \frac{20 ( - 676 + 52 i + 1 )}{26 i ( - 676 + 52 i + 100 )} \overset{◯}{6} \overset{◯}{7} \frac{20 ( 52 i - 675 )}{26 i ( 52 i - 576 )} \overset{◯}{8} \overset{◯}{9} \frac{1040 i - 13500}{1352 i ^{2} - 14976 i} \overset{◯}{10} \frac{1040 i - 13500}{- 1352 - 14976 i} \overset{◯}{11} \frac{1287 - 97876 i}{108706}$
①	Find $(26 i + 1)^{2}$ using formula. $(A + B)^{2} = A^{2} + 2 \cdot A \cdot B + B^{2}$ where $A = 26 i$ and $B = 1$ . $(26 i + 1)^{2} = (26 i)^{2} + 2 \cdot 26 i \cdot 1 + 1^{2} = 676 i^{2} + 52 i + 1$
②	$(26 i)^{2} = 2 6^{2} i^{2} = 676 i^{2}$
③	$2 \cdot 26 i = 52 i$
④	$676 i^{2} = 676 \cdot (- 1) = - 676$
⑤	$676 i^{2} = 676 \cdot (- 1) = - 676$
⑥	Combine like terms: $- 676 + 52 i + 1 = 52 i - 675$
⑦	Combine like terms: $- 676 + 52 i + 100 = 52 i - 576$
⑧	Multiply $20$ by $(52 i - 675)$ $20 \cdot (52 i - 675) = 1040 i - 13500$
⑨	Multiply $26 i$ by $(52 i - 576)$ $26 i \cdot (52 i - 576) = 1352 i^{2} - 14976 i$
⑩	$1352 i^{2} = 1352 \cdot (- 1) = - 1352$
⑪	Divide $- 13500 + 1040 i$ by $- 1352 - 14976 i$ to get $\frac{1287 - 97876 i}{108706}$ . ( view steps )

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