# Complex Number Question (Easy)

1. May 6, 2016

### David Donald

1. The problem statement, all variables and given/known data
Verify that i2=-1
using

2. Relevant equations

3. The attempt at a solution
I tried choosing coefficients so that it would be (i)(i) = (0 - 1)+(0+0)i = -1
so then I get i^2 = -1

But I was told that this was wrong and to try again...

Can anyone explain what I did was wrong or if
theirs a smarter way to verify?

2. May 6, 2016

### Math_QED

We define i as the root of -1. So $$i^2 = -1$$ is true, no need to verify this.

The following statement is false: $$(a+bi)(c+di) = (ac-bd)(ad+bc)i$$
This would mean that the product of 2 complex numbers is an imaginary number. This is false. For example, $$i * i = i^2 = -1$$ is a real number.

What is $$(a+bi)(c+di)$$ equal to, using distributivity and $$i^2 = -1$$

Last edited: May 6, 2016
3. May 6, 2016

### Staff: Mentor

Are you sure that you have written the equation above correctly? As already noted by Math_QED, this is false.

4. May 6, 2016

### PeroK

It's supposed to be:

$(a+bi)(c+di) = (ac-bd) + (ad+bc)i$

And, assuming this holds for all $a, b, c, d$ show that $i^2 = -1$.

That's what I assume the exercise to be.

5. May 7, 2016

### Staff: Mentor

But the whole point of this exercise is to prove this. In other words, the OP can't use this definition.

All,
Let's sit back and see what the OP says...