Systems over the complex field

Task number: 2479

Solve the following systems over the field of complex numbers \(\mathbb C\).

  • Variant 1

    \( \begin{array}{rlrlr} x_1 &+& i x_2 &=\ & i \\ i x_1 &+& (1-i) x_2 &=\ & -1 \end{array} \)

  • Variant 2

    \( \begin{array}{rlrlrlr} 2 x_1 &+& (2+2i) x_2 &+& 2i x_3 &= & 1 \\ (1-i) x_1 &+& (1+3i) x_2 &+& (i-1) x_3 &= & 0 \\ (1+i) x_1 &+& (1-i) x_2 &+& (1+i) x_3 &= & 1 \end{array} \)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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