Question

slove this guys explanation pls​

Answer 1

❏Question :-

$\rm \: simplify : \\ \to \: {(1 + i)}^{4} { \bigg(1 + \frac{1}{i} \bigg)}^{4}$

❏Answer :-

$\to \: \boxed{{(1 + i)}^{4} { \bigg(1 + \frac{1}{i} \bigg)}^{4} = 16} \:$

→ Option (C) is correct .

❏Solution :-

We have,

$\mapsto \: {(1 + i)}^{4} { \bigg(1 + \frac{1}{i} \bigg)}^{4} \: \\ \\ \mapsto \: {(1 + i)}^{4} { \bigg( \frac{i + 1}{i} \bigg)}^{4} \: \\ \\ \mapsto \: {(1 + i)}^{4} \frac{ {(1 + i)}^{4} }{ {i}^{4} } \\ \\ \because \: i = \sqrt{ - 1} \\ \\ so \: \: \: {i}^{2} = - 1 \: \: \: and \: \: \: {i}^{4} = 1 \\ \\ \mapsto \: {(1 + i)}^{4} \frac{ {(1 + i)}^{4} }{1} \\ \\ \mapsto \: {(1 + i)}^{8} \\ \\ \rm \: we \: can \: write \: it \: \\ \\ \mapsto \: { \{ {(1 + i)}^{2} \} }^{4} \\ \\ \mapsto \: { \{ {1}^{2} + {i}^{2} + 2i\}}^{4} \: \: \because \: {i}^{2} = - 1 \\ \\ \mapsto \: { \{ \: 1 - 1 + 2i \}}^{4} \\ \\ \mapsto \: {(2i)}^{4} \\ \\ \mapsto \: {2}^{4} \times {i}^{4} \: \: \: \: \because \: {i}^{4} = 1 \\ \\ \mapsto \: {2}^{4} = 16 \\ \\ \to \: \boxed{{(1 + i)}^{4} { \bigg(1 + \frac{1}{i} \bigg)}^{4} = 16}$

Option (c) is correct .