The correct option is B 2i i+i^2+i^3+i^4=0 i^2= 1 #160;; i^3= #160; i ; i^4= #160; #160;+1 ∴ (1+i^5)(1+i) =(1+i^4i)(1+i) ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Complex Numbers

1+i+i2+i3+i4+...

Question

$(1 + i + i^{2} + i^{3} + i^{4} + i^{5}) (1 + i) =$

i

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2 i

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3 i

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4 i

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Solution

The correct option is B $2 i$
$i + i^{2} + i^{3} + i^{4} = 0$
$i^{2} = - 1; i^{3} = - i; i^{4} = + 1$
$∴ (1 + i^{5}) (1 + i)$
$= (1 + i^{4} i) (1 + i)$
$= (1 + i) (1 + i)$
$= (1 + i)^{2}$
$= 1 - 1 + 2 i$
$= 2 i$

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I_{n} = \int_{0}^{π / 4} {tan}^{n} d x,

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is :

Express the following complex numbers in the standard form a + i b :

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