Question

The value of 1+1+i+(1+i)^2+(1+i)^3?
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Answer 1

Answer:

5i

Step-by-step explanation:

Given :

$1 + (1 + i) \: + {(1 + i)}^{2} + {(1 + i)}^{3}$

Here,

${(1 + i)}^{2} = 1 + {i}^{2} + 2i \\ = 1 - 1 + 2i \\ = 2i \\ and \\ {(1 + i)}^{3} = {(1 + i)}^{2} \times (1 + i) \\ = 2i \times (1 + i) \\ = 2i + 2 {i}^{2} \\ = 2i - 2$

Therefore,

$1 + (1 + i) + {(1 + i)}^{2} + {1 + i)}^{3} \\ = 2 + i + 2i + 2i - 2 \\ = 5i$

$Note : \: {i}^{2} = - 1$

Hence, the answer is 5i