Question

Q8. The value of (1 + i)4 + (1 - 1)4 is
(a) 8 (6) 4 (c) -8(d) -4​

Answer 1

Answer:

$\large\boxed{\sf{(c)\;-8}}$

Step-by-step explanation:

${(1 + i)}^{4} + {(1 - i)}^{4} \\ \\ = {( {(1 + i)}^{2} )}^{2} + {( {(1 - i)}^{2}) }^{2} \\ \\ = {(1 + 2i + {i}^{2}) }^{2} + {(1 - 2i + {i}^{2}) }^{2} \\ \\ = {(1 + 2i - 1)}^{2} + {(1 - 2i - 1)}^{2} \\ \\ = {(2i)}^{2} + {( - 2i)}^{2} \\ \\ = 4 {i}^{2} + 4 {i}^{2} \\ \\ = 8 {i}^{2} \\ \\ = 8 \times ( - 1) \\ \\ = - 8$

Concept Map :-

• ${i}^{2} = - 1$

• ${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

• ${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$