This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Ili kutatua mlinganyo x(1+j)^2 + y(2-j)^2 = 3+10j kwa x na y, tutafuata hatua hizi: Hatua ya 1: Panua vigawo vya namba changamano. Panua (1+j)^2: (1+j)^2 = 1^2 + 2(1)(j) + j^2 = 1 + 2j - 1 = 2j Panua (2-j)^2: (2-j)^2 = 2^2 - 2(2)(j) + j^2 = 4 - 4j - 1 = 3 - 4j Hatua ya 2: Badilisha vigawo vilivyopanuliwa kwenye mlinganyo asilia. x(2j) + y(3-4j) = 3+10j 2xj + 3y - 4yj = 3+10j Hatua ya 3: Panga sehemu halisi na sehemu za kufikirika za mlinganyo. Panga upande wa kushoto: Sehemu halisi: 3y Sehemu ya kufikirika: 2xj - 4yj = (2x - 4y)j Hivyo mlinganyo unakuwa: 3y + (2x - 4y)j = 3+10j Hatua ya 4: Linganisha sehemu halisi na sehemu za kufikirika kutoka pande zote mbili za mlinganyo. Kulinganisha sehemu halisi: 3y = 3 (Mlinganyo 1) Kulinganisha sehemu za kufikirika: 2x - 4y = 10 (Mlinganyo 2) Hatua ya 5: Tatua mfumo wa milinganyo. Kutoka Mlinganyo 1: 3y = 3 y = (3)/(3) y = 1 Badilisha y=1 kwenye Mlinganyo 2: 2x - 4(1) = 10 2x - 4 = 10 2x = 10 + 4 2x = 14 x = (14)/(2) x = 7 Hatua ya 6: Andika majibu ya mwisho. Thamani za x na y ni: x=7, y=1 That's 2 down. 3 left today — send the next one.