Question

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Answer 1

Question :–

• If x = (1 + i) , then find the value of (x - 1)⁴ + 4 .

ANSWER :–

▪︎ (x - 1)⁴ + 4 = 5

EXPLANATION :–

GIVEN :–

• Value of x = (1 + i).

TO FIND :–

• Value of (x - 1)⁴ + 4 = ?

SOLUTION :–

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

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

$\\ \: = \: {i}^{4} + 4$

Properties of iota :–

$\\ { \: \: \: \: \: { \huge{.}} \: \: \: \: \: i = \sqrt{ - 1} }$

$\\ { \: \: \: \: \: { \huge{.}} \: \: \: \: \: i {}^{2} = { - 1} }$

$\\ { \: \: \: \: \: { \huge{.}} \: \: \: \: \: i {}^{3} = { - i} }$

$\\ { \: \: \: \: \: { \huge{.}} \: \: \: \: \: i {}^{4} = { 1} }$

• So that –

$\\ \: = \: 1 + 4 \: \: \: \: \: \: \: \:[ \: \: \because \: \: \: {i}^{4} = 1 ]$

$\\ \: = \: 5 \: \:$

Hence , $\: \: {(x - 1)}^{4} + 4= \: 5 \: \:$

$\\ \rule{220}{2}$