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Algebra Level 1

what is the sum of all solutions of x²+1=0 ?

2 solutions

Ajay Krishnaswamy
May 5, 2015

The solution to this problem is simple.

Using completing the square, we get:

x^2 = -1

x = +-sqrt(-1)

x = positive i or negative i

Add these two solutions up:

i + -i

i - i

There is no positive or negative i .

Because $\pm i > 0$ .

Then it equals $-1 > 0$ .

. . - 3 months ago

. .
Mar 15, 2021

$x ^ { 2 } + 1 = 0 \rightarrow ( x + i ) ( x - i ) = 0 \rightarrow x = -i, x = i \rightarrow i + ( -i ) = i - i = \boxed { 0 }$ .