Question

find the value of (1+i) whole power 16​

Answer 1

the answer will be 1+i^16

Answer 2

Given: A complex  number 1+ i

To find: $(1+i)^{16}$

Step-by-step explanation:

As given

$(1+i)^{16}$ can be written as

$((1+i)^2)^8 \text {---} [\because (a^m)^n+a^{mn}]$

Now as we know

$(a+b)^2= a^2+b^2+2ab$ we have

$(1^1+i^2+2\times 1\times i)^8$

Now $i^2= -1$ we get

$(1-1+2i)^8\\\\=(2i)^8=2^8\times (i^2)^4= 256 \times (-1)^4= 256\times 1 =256$

Hence the value of $(1+i)^{16}$ is 256