Question

the value of (1+i/1-i)^4 is​

Answer 1

Answer:

−8

Step-by-step explanation:

(1+i) 4 +(1−i) 4

⇒ [(1+i) 2 ] 2 +[(1−i) 2 ] 2

We know, (a+b) 2

=a 2+2ab+b 2 and (a−b) 2

= 2 −2ab+b 2

⇒ [1+2i+i 2 ] 2 +[1−2i+i 2 ] 2

⇒ [1+2i−1] 2 +[1−2i−1] 2

2 =[i−1 ]

⇒ (2i) 2 +(−2i) 2

⇒ 4i 2 +4i 2

⇒ −4−4

⇒ −8

∴ (1+i) 4 +(1−i) 4 =−8

Answer 2

Answer:

(1+i) 4 +(1−i) 4

⇒ [(1+i) 2] 2 +[(1−i) 2 ] 2

We know, (a+b)

2 =a 2 +2ab+b 2 and (a−b) 2 =2−2ab+b

⇒ [1+2i+i 2 ] 2 +[1−2i+i 2] 2

⇒ [1+2i−1] 2 +[1−2i−1] 2 [ i 2=−1 ]

⇒ (2i) 2+(−2i) 2

⇒ 4i 2 +4i 2

⇒ −4−4

⇒ −8

∴ (1+i) 4+(1−i) 4 =−8

Step-by-step explanation:

pls make me as a brainlist