Issolvi z=frac{3sqrt{3}-3i}{2sqrt{3}i}

$$z = \frac { 3 \sqrt { 3 } - 3 i } { 2 \sqrt { 3 } i }$$

Solvi għal z

$$z=-\frac{\sqrt{3}}{2}-\frac{3}{2}i\approx -0.866025404-1.5i$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Irrazzjonalizza d-denominatur tal-\frac{3\sqrt{3}-3i}{2i\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$z=\frac{\left(3\sqrt{3}-3i\right)\sqrt{3}}{2i\left(\sqrt{3}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$z=\frac{\left(3\sqrt{3}-3i\right)\sqrt{3}}{2i\times 3}$$

Immultiplika 2i u 3 biex tikseb 6i.

$$z=\frac{\left(3\sqrt{3}-3i\right)\sqrt{3}}{6i}$$

Uża l-propjetà distributtiva biex timmultiplika 3\sqrt{3}-3i b'\sqrt{3}.

$$z=\frac{3\left(\sqrt{3}\right)^{2}-3i\sqrt{3}}{6i}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$z=\frac{3\times 3-3i\sqrt{3}}{6i}$$

Immultiplika 3 u 3 biex tikseb 9.

$$z=\frac{9-3i\sqrt{3}}{6i}$$

Iddividi kull terminu ta' 9-3i\sqrt{3} b'6i biex tikseb\frac{9}{6i}+\frac{-3i\sqrt{3}}{6i}.

$$z=\frac{9}{6i}+\frac{-3i\sqrt{3}}{6i}$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{9}{6i} bl-unità immaġinarja i.

$$z=\frac{9i}{6i^{2}}+\frac{-3i\sqrt{3}}{6i}$$

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

$$z=\frac{9i}{-6}+\frac{-3i\sqrt{3}}{6i}$$

Iddividi 9i b'-6 biex tikseb-\frac{3}{2}i.

$$z=-\frac{3}{2}i+\frac{-3i\sqrt{3}}{6i}$$

Iddividi -3i\sqrt{3} b'6i biex tikseb-\frac{1}{2}\sqrt{3}.

$$z=-\frac{3}{2}i-\frac{1}{2}\sqrt{3}$$

Assenja z

$$z≔-\frac{\sqrt{3}}{2}-\frac{3}{2}i$$