Issolvi 6i/7-3i

$$\frac { 6 i } { 7 - 3 i }$$

Evalwa

$$-\frac{9}{29}+\frac{21}{29}i\approx -0.310344828+0.724137931i$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur bil-konjugat kumpless tad-denominatur, 7+3i.

$$\frac{6i\left(7+3i\right)}{\left(7-3i\right)\left(7+3i\right)}$$

Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{6i\left(7+3i\right)}{7^{2}-3^{2}i^{2}}$$

Skont id-definizzjoni, i^{2} huwa -1. Ikkalkula d-denominatur.

$$\frac{6i\left(7+3i\right)}{58}$$

Immultiplika 6i b'7+3i.

$$\frac{6i\times 7+6\times 3i^{2}}{58}$$

Skont id-definizzjoni, i^{2} huwa -1.

$$\frac{6i\times 7+6\times 3\left(-1\right)}{58}$$

Agħmel il-multiplikazzjonijiet fi 6i\times 7+6\times 3\left(-1\right). Erġa' ordna t-termini.

$$\frac{-18+42i}{58}$$

Iddividi -18+42i b'58 biex tikseb-\frac{9}{29}+\frac{21}{29}i.

$$-\frac{9}{29}+\frac{21}{29}i$$

Parti Reali

$$-\frac{9}{29} = -0.3103448275862069$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{6i}{7-3i} bil-konjugat kumpless tad-denominatur, 7+3i.

$$Re(\frac{6i\left(7+3i\right)}{\left(7-3i\right)\left(7+3i\right)})$$

Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$Re(\frac{6i\left(7+3i\right)}{7^{2}-3^{2}i^{2}})$$

Skont id-definizzjoni, i^{2} huwa -1. Ikkalkula d-denominatur.

$$Re(\frac{6i\left(7+3i\right)}{58})$$

Immultiplika 6i b'7+3i.

$$Re(\frac{6i\times 7+6\times 3i^{2}}{58})$$

Skont id-definizzjoni, i^{2} huwa -1.

$$Re(\frac{6i\times 7+6\times 3\left(-1\right)}{58})$$

Agħmel il-multiplikazzjonijiet fi 6i\times 7+6\times 3\left(-1\right). Erġa' ordna t-termini.

$$Re(\frac{-18+42i}{58})$$

Iddividi -18+42i b'58 biex tikseb-\frac{9}{29}+\frac{21}{29}i.

$$Re(-\frac{9}{29}+\frac{21}{29}i)$$

Il-parti reali ta' -\frac{9}{29}+\frac{21}{29}i hija -\frac{9}{29}.

$$-\frac{9}{29}$$