Question

Why is it that if you multiply a negative imaginary number (-i) by a positive imaginary number (i), it equals to positive 1? Shouldn’t it be a negative 1?

-(-1) • (-1) = -1
This is the right equation, right?

Answer 1

Hi there!

Unfortunately, that's not the right equation. I'll help show you the proper steps.

So, first, let's define i.

i = √(-1)

Now, let's multiply -i and i

(-i)(i)

Substitute the value of i

- √(-1) * √(-1)

Let's add a parenthesis using the associative property of multiplication

- [ √(-1) * √(-1) ]

Multiplying two same square roots eliminates the square root symbol.

- (-1)

A negative of a negative is positive

= 1

Thus, a negative imaginary number multiplied with a positive imaginary number equals positive 1.

Have an awesome day! :)

Answer 2

`(-i)i =-ii`Once we multiply the negative imaginary number (-i) to the positive imaginary number (i),

`\left(-i\right)(i)`

`\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a`

`(-i)i =-ii`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)`

`ii=\:i^(1+1)=\:i^2\\ -ii=-i^2`

`\mathrm{Apply\:imaginary\:number\:rule}:\quad \:i^2=-1`

`-i^2=-(-1)`

Which is equal to 1.

so multiply a negative imaginary number (-i) by a positive imaginary number (i), it equals to positive 1.