Riješi -3/2+3i/2/sqrt{2}

$$- \frac { \frac { 3 } { 2 } + \frac { 3 i } { 2 } } { \sqrt { 2 } }$$

Izračunaj

$$\sqrt{2}\left(-\frac{3}{4}-\frac{3}{4}i\right)\approx -1,060660172-1,060660172i$$

Koraci rješenja

Podijelite 3i s 2 da biste dobili \frac{3}{2}i.

$$-\frac{\frac{3}{2}+\frac{3}{2}i}{\sqrt{2}}$$

Racionalizirajte nazivnik \frac{\frac{3}{2}+\frac{3}{2}i}{\sqrt{2}} množenje brojnik i nazivnik \sqrt{2}.

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

Kvadrat od \sqrt{2} je 2.

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

Podijelite \left(\frac{3}{2}+\frac{3}{2}i\right)\sqrt{2} s 2 da biste dobili \left(\frac{3}{4}+\frac{3}{4}i\right)\sqrt{2}.

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

Pomnožite -1 i \frac{3}{4}+\frac{3}{4}i da biste dobili -\frac{3}{4}-\frac{3}{4}i.

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

Realni dio

$$-\frac{3 \sqrt{2}}{4} = -1,0606601717798214$$