(1+i)3+(1-i)3

Question

(1+i)3+(1-i)3  (A)  1  (B)  -2  (C)  0  (D)  -4

Tardigrade Admin · Accepted Answer

(1+i)3+(1-i)3=(1+i)2(1+i)+(1-i)2(1-i) =(1+i2+2i)(1+i)+(1+i2-2i) (1-i) [ beginalign ∵ (a+b)2=a2+b2+2ab (a-b)2=a2+b2-2ab endalign ] =2i(1+i)+(-2i)(1-i) (∵ i2=-1) =2i+2i2-2i+2i2 =4i2=-4 (∵ i2=-1)

Q. $(1 + i)^{3} + (1 - i)^{3}$

$1$

$- 2$

$0$

$- 4$

Q. (1+i)3+(1−i)3

1

−2

0

−4

(1+i)3+(1−i)3=(1+i)2(1+i)+(1−i)2(1−i) =(1+i2+2i)(1+i)+(1+i2−2i)(1−i) [​∵(a+b)2=a2+b2+2ab(a−b)2=a2+b2−2ab​] =2i(1+i)+(−2i)(1−i) (∵i2=−1) =2i+2i2−2i+2i2 =4i2=−4 (∵i2=−1)

Q. $(1 + i)^{3} + (1 - i)^{3}$

$1$

$- 2$

$0$

$- 4$