Question

Find the value of (1 +i)16​

Answer 1

Answer:

Given: A complex number 1+ i

To find: (1 + i) 16

Step-by-step explanation:

As given

16 (1 + i)¹6 can be written as

((1 + i)²)8[: (am)n + amn]

Now as we know

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

(1¹ + ² + 2 × 1 × i)8

Now

i ^ 2 = - 1

we get

(1 - 1 + 2i)8

= (21)8 = 28 × (₁²) 4 = 256 × (-1)¹ = 256 × 1 = 256 X

Hence the value of (1 + i)¹6 is 256

hope it's helpful

Step-by-step explanation:

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Answer 2

Answer:

Simplifying (1+i)6+(1−i)6.

(1+i)6+(1−i)6=((1+i)2)3+((1−i)2)3

=(1+i2+2i)3+(1+i2−2i)3

=(1−1+2i)3+(1−1−2i)3

=8i3−8i3

=8(−i)−8(−i)

=−8i+8i

=0