Definition:Complex Arithmetic
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Definition
Complex arithmetic is the branch of arithmetic which concerns the manipulation of complex numbers
Examples
Example: $\dfrac {\paren {1 + 2 i}^2} {1 - i}$
- $\dfrac {\paren {1 + 2 i}^2} {1 - i} = -\dfrac 7 2 + \dfrac 1 2 i$
Example: $\dfrac 1 {1 + i} + \dfrac 1 {1 - 2 i}$
- $\dfrac 1 {1 + i} + \dfrac 1 {1 - 2 i} = \dfrac 7 {10} - \dfrac 1 {10} i$
Example: Sum of Powers of $i$ from $0$ to $7$
- $1 + i + i^2 + i^3 + i^4 + i^5 + i^6 + i^7 = 0$
Example: $\dfrac 1 {\paren {4 + 2 i} \paren {2 - 3 i} }$
- $\dfrac 1 {\paren {4 + 2 i} \paren {2 - 3 i} } = \dfrac 7 {130} + \dfrac {2 i} {65}$
Example: $\dfrac {5 + 5 i} {3 - 4 i} + \dfrac {20} {4 + 3 i}$
- $\dfrac {5 + 5 i} {3 - 4 i} + \dfrac {20} {4 + 3 i} = 3 - i$
Example: $\dfrac {3 i^{30} - i^{19} } {2 i - 1}$
- $\dfrac {3 i^{30} - i^{19} } {2 i - 1} = 1 + i$
Also see
- Results about complex arithmetic can be found here.