The value of $1 + (1 + i) + (1 + i)^{2} + (1 + i)^{3} =$

0

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5 i

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4 i

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3 i

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Solution

The correct option is B $5 i$
$(1 + i)^{2} = 1 - 1 + 2 i$
$= 2 i$
$(1 + i)^{3} = (1 + i)^{2} (1 + i)$
$= 2 i (1 + i)$
$= 2 i - 2$
$∴ 1 + (1 + i) + (1 + i)^{2} + (1 + i)^{3}$
$= 1 + 1 + i + 2 i + 2 i - 2$
$= 5 i$

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The value of 1+(1+i)+(1+i)2+(1+i)3=

The correct option is B 5i(1+i)2=1−1+2i=2i(1+i)3=(1+i)2(1+i)=2i(1+i)=2i−2∴1+(1+i)+(1+i)2+(1+i)3=1+1+i+2i+2i−2=5i

The value of $1 + (1 + i) + (1 + i)^{2} + (1 + i)^{3} =$

The correct option is B $5 i$
$(1 + i)^{2} = 1 - 1 + 2 i$
$= 2 i$
$(1 + i)^{3} = (1 + i)^{2} (1 + i)$
$= 2 i (1 + i)$
$= 2 i - 2$
$∴ 1 + (1 + i) + (1 + i)^{2} + (1 + i)^{3}$
$= 1 + 1 + i + 2 i + 2 i - 2$
$= 5 i$