Math 2.0

statement proposition

i squared is minus one

Statement

Let ii be the imaginary unit of C\mathbb{C}. Then i2=−1i^2 = -1.

Remarks

With the product of complex numbers, (0+1i)(0+1i)=(0⋅0−1⋅1)+(0⋅1+1⋅0)i=−1(0 + 1 i)(0 + 1 i) = (0 \cdot 0 - 1 \cdot 1) + (0 \cdot 1 + 1 \cdot 0) i = -1. Also (−i)2=−1(-i)^2 = -1. Thus −1-1 has the two square roots ii and −i-i in C\mathbb{C}.

Explanations

L1 human

This is the property that defines ii. All the rules for computation with complex numbers come from the usual rules of algebra together with i2=−1i^2 = -1.

What this node needs for W1
  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a node is. They do not measure its truth.

What this needs

To read this node, read these 3 nodes in this order. The foundations come first, and the list ends with this node.

Complex numbers, object, no evidence levelComplex numbersobjectImaginary unit, object, no evidence levelImaginary unitobjecti squared is minus one, statement, no evidence leveli squared is minus onestatement
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Complex numbers object
  2. Imaginary unit object
  3. i squared is minus one statement

What depends on this

1 node uses this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Imaginary_unit, Definition

What links here

Used by