Issolvi 1/2+3i

$$\frac { 1 } { 2 + 3 i }$$

Evalwa

$$\frac{2}{13}-\frac{3}{13}i\approx 0.153846154-0.230769231i$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur bil-konjugat kumpless tad-denominatur, 2-3i.

$$\frac{1\left(2-3i\right)}{\left(2+3i\right)\left(2-3i\right)}$$

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}.

$$\frac{1\left(2-3i\right)}{2^{2}-3^{2}i^{2}}$$

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

$$\frac{1\left(2-3i\right)}{13}$$

Immultiplika 1 u 2-3i biex tikseb 2-3i.

$$\frac{2-3i}{13}$$

Iddividi 2-3i b'13 biex tikseb\frac{2}{13}-\frac{3}{13}i.

$$\frac{2}{13}-\frac{3}{13}i$$

Parti Reali

$$\frac{2}{13} = 0.15384615384615385$$

Passi tas-Soluzzjonijiet

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{1}{2+3i} bil-konjugat kumpless tad-denominatur, 2-3i.

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

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}.

$$Re(\frac{1\left(2-3i\right)}{2^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{1\left(2-3i\right)}{13})$$

Immultiplika 1 u 2-3i biex tikseb 2-3i.

$$Re(\frac{2-3i}{13})$$

Iddividi 2-3i b'13 biex tikseb\frac{2}{13}-\frac{3}{13}i.

$$Re(\frac{2}{13}-\frac{3}{13}i)$$

Il-parti reali ta' \frac{2}{13}-\frac{3}{13}i hija \frac{2}{13}.

$$\frac{2}{13}$$