Question

How is multiplying 3-2i by i^2 represented on the complex plane?

Answer 1

Answer:

The equation is represented 3 units to the left of the complex plane and 2 units up.

Explanation:

Well to see how this is represented, we first need to multiply it out so we can see how it looks when it is simplified!

$(3-2i)(i^2)\\\i^2=-1\\(3-2i)(-1)\\-(3-2i) *1\\-3+2i!$

We know that on a complex plane, our imaginary numbers are represented on the vertical axis.

So the original expression, (3-2i) would have been 3 units to the right on a complex graph and 2 units downward!

The equation I input above should be pretty straightforward, but one thing I didn't mention was that i^2 should = -1 when dealing with complex numbers!

Therefore, the equation 3-2i * i^2 is equal to -3 + 2i, this is graphed 3 units to the left and to units upward!

If you notice, this is the exact opposite of the original equation! Why? Well it's because we simply multiplied by negative 1!