File tree Expand file tree Collapse file tree 1 file changed +11
-1
lines changed
exercises/complex-numbers Expand file tree Collapse file tree 1 file changed +11
-1
lines changed Original file line number Diff line number Diff line change @@ -26,6 +26,8 @@ The absolute value (or modulus) of `z` is defined as:
2626|z| = sqrt(a^2 + b^2)
2727```
2828
29+ ### Sqaure
30+
2931The square of the absolute value, ` |z|² ` , can be computed as the product of ` z ` and its conjugate:
3032
3133``` plaintext
@@ -58,12 +60,20 @@ The product of two complex numbers is defined as:
5860z₁ * z₂ = (a + b * i) * (c + d * i) = (a * c - b * d) + (b * c + a * d) * i
5961```
6062
63+ ### Reciprocal
64+
65+ The reciprocal of a non-zero complex number is given by:
66+
67+ ``` math
68+ 1 / z = 1 / (a + b * i) = a / (a² + b²) - b / (a² + b²) * i
69+ ```
70+
6171### Division
6272
6373The division of one complex number by another is given by:
6474
6575``` plaintext
66- z₁ / z₂ = (a + b * i) / (c + d * i) = (a * c + b * d) / (c² + d²) + (b * c - a * d) / (c² + d²) * i
76+ z₁ / z₂ = z₁ * (1 / z₂) = (a + b * i) / (c + d * i) = (a * c + b * d) / (c² + d²) + (b * c - a * d) / (c² + d²) * i
6777```
6878
6979### Exponentiation
You can’t perform that action at this time.
0 commit comments