Issolvi 2+3i/5-4i

$$\frac{ 2+3i }{ 5-4i }$$

Evalwa

$$-\frac{2}{41}+\frac{23}{41}i\approx -0.048780488+0.56097561i$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur bil-konjugat kumpless tad-denominatur, 5+4i.

$$\frac{\left(2+3i\right)\left(5+4i\right)}{\left(5-4i\right)\left(5+4i\right)}$$

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}.

$$\frac{\left(2+3i\right)\left(5+4i\right)}{5^{2}-4^{2}i^{2}}$$

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

$$\frac{\left(2+3i\right)\left(5+4i\right)}{41}$$

Immutiplika in-numri kumplessi 2+3i u 5+4i bl-istess mod kif timmultiplika binomials.

$$\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4i^{2}}{41}$$

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

$$\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right)}{41}$$

Agħmel il-multiplikazzjonijiet fi 2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right).

$$\frac{10+8i+15i-12}{41}$$

Ikkombina l-partijiet reali u immaġinarji f'10+8i+15i-12.

$$\frac{10-12+\left(8+15\right)i}{41}$$

Agħmel l-addizzjonijiet fi 10-12+\left(8+15\right)i.

$$\frac{-2+23i}{41}$$

Iddividi -2+23i b'41 biex tikseb-\frac{2}{41}+\frac{23}{41}i.

$$-\frac{2}{41}+\frac{23}{41}i$$

Parti Reali

$$-\frac{2}{41} = -0.04878048780487805$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{2+3i}{5-4i} bil-konjugat kumpless tad-denominatur, 5+4i.

$$Re(\frac{\left(2+3i\right)\left(5+4i\right)}{\left(5-4i\right)\left(5+4i\right)})$$

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}.

$$Re(\frac{\left(2+3i\right)\left(5+4i\right)}{5^{2}-4^{2}i^{2}})$$

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

$$Re(\frac{\left(2+3i\right)\left(5+4i\right)}{41})$$

Immutiplika in-numri kumplessi 2+3i u 5+4i bl-istess mod kif timmultiplika binomials.

$$Re(\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4i^{2}}{41})$$

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

$$Re(\frac{2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right)}{41})$$

Agħmel il-multiplikazzjonijiet fi 2\times 5+2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right).

$$Re(\frac{10+8i+15i-12}{41})$$

Ikkombina l-partijiet reali u immaġinarji f'10+8i+15i-12.

$$Re(\frac{10-12+\left(8+15\right)i}{41})$$

Agħmel l-addizzjonijiet fi 10-12+\left(8+15\right)i.

$$Re(\frac{-2+23i}{41})$$

Iddividi -2+23i b'41 biex tikseb-\frac{2}{41}+\frac{23}{41}i.

$$Re(-\frac{2}{41}+\frac{23}{41}i)$$

Il-parti reali ta' -\frac{2}{41}+\frac{23}{41}i hija -\frac{2}{41}.

$$-\frac{2}{41}$$