Question

(1+i)^4 (1+1/i)^4 = 16
proved this question please fast​

Answer 1

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

$\displaystyle \: {(1 + i)}^{4} + {(1 + \frac{1}{i}) }^{4}$

$= \displaystyle \: {(1 + i)}^{4} + {(1 + \frac{i}{ {i}^{2} }) }^{4}$

$= \displaystyle \: {(1 + i)}^{4} + {(1 - i) }^{4}$

$= \displaystyle \: {(1 + {i}^{2} + 2i)}^{2} + {(1 + {i}^{2} - 2i)}^{2}$

$= \displaystyle \: {(1 - 1 + 2i)}^{2} + {(1 - 1 - 2i)}^{2}$

$= \displaystyle \: {( 2i)}^{2} + {( - 2i)}^{2}$

$= 4 {i}^{2} + 4 {i}^{2}$

$= 8 {i}^{2}$

$= 8 \times ( - 1)$

$= - 8$

$</p><p></p><p>\displaystyle\textcolor{red}{Please \: Mark \: it \: Brainliest}$

Answer 2

Answer:

Given:

The equation is,

(1+i)⁴×(1+i/i)⁴=16

Solution:

First take LHS,

(1+i)⁴×(1+i)⁴/i⁴

As we know that,

i²=-1

i⁴=(-1)²=1

Now,

→ (1+i)⁴×(1+i)⁴

→(1+i)⁸

Multiply and divide by √2 .

→(√2(1/√2+i/√2))⁸

→2⁴(cosπ/4+i sinπ/4)⁸

→16(cos8π/4+isin8π/4)

→16(cos2π+isin2π)

→16(1-0)

→16

Step-by-step explanation:

Hope it helps you.......