# Is 1+i>-1+i?

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This is part of a series on common misconceptions.

True or False?\[1+i>-1+i\]

**Why some people say it's true:** Subtract \(i\) from both sides, and we will have \(1>-1\), which is obviously true.

**Why some people say it's false:** (Explanation)

The statement is \( \color{red}{\textbf{false}}\).

Proof:

Let's assume it's true, i.e. \(1+i>-1+i.\)

Squaring both sides gives \(1+i^2+2i>-1+i^2-2i,\) which on further simplification gives \(2i>-2-2i.\)

Rearranging, \(4i>-2.\)

Dividing by 2 throughout gives \(2i>-1.\)

Squaring LHS and RHS again, we have \(4i^2>1,\) which gives \(-4>1.\)

This is clearly false, hence a contradiction to our original statement.

Therefore, the given statement is false. \(_\square\)

Rebuttal: This doesn’t make sense.

Reply: Imaginary numbers don’t operate in the same way as real numbers

Rebuttal:

Reply:

**See Also**