Question

express the following on the form of a+ib a,b€Ri find value of a and b
$\binom{1 + i}{1 - i {}^{} } {}^{2}$
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Answer 1

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□ To find the value of

$\large\bold\red{ {( \frac{1 + i}{1 - i}) }^{2} }$

♡ Formula used

◇ i² = - 1

◇ Solution :-

${( \frac{1 + i}{1 - i}) }^{2} \\ = {( \frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i} )}^{2} \\ = { (\frac{ {(1 + i)}^{2} }{ {1}^{2} - {i}^{2} }) }^{2} \\ = { (\frac{ {1}^{2} + { i}^{2} + 2i }{1 - ( - 1)}) }^{2} \\ = {( \frac{1 - 1 + 2i}{1 + 1}) }^{2} \\ = {( \frac{2i}{2} )}^{2} \\ = {i}^{2} \\ = - 1 \\ = - 1 + 0i \\ so \: on \: comparing \: with \: a + ib \\ we \: get \: a = - 1 \: and \: b = 0$

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Answer 2

Answer:

this is correct.............................