An algebra problem by Naman Kapoor

Algebra Level 2

Find the value of i + i \sqrt{i} +\sqrt{-i}

1 -1 -i √2

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2 solutions

Rishi Hazra
Nov 2, 2014

this is how I proceeded................

(-i) can be written as (i)^3

thus i ^1/2 + (-i) ^1/2 = i ^ 1/2 + i ^3/2

let this be equal to x

therefore

x= i ^ 1/2 + i ^ 3/2

squaring both sides, we get

x^2= i + (-i) + 2*(i ^2)

x^2= -2

now, in order to obtain x, I took the square root on both side which gave

x=(2^ 1/2)*i

Roland Casuga
Nov 2, 2014

Using d'moivre theorem..i^1/2=(1angle90)^1/2=(1^1/2)angle(1/2*90)=1angle 45

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