# 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 $\color{#D61F06}{\textbf{false}}$.

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**