सोडोवचें 240/25+25sqrt{3i+10+sqrt{300}i}

$$\frac{ 240 }{ 25+25 \sqrt{ 3 } i+10+ \sqrt{ 300 } i }$$

मूल्यांकन करचें

$$\frac{48}{7\left(1+\sqrt{3}i\right)}\approx 1.714285714-2.969229956i$$

सोडोवणी पांवडे

35 मेळोवंक 25 आनी 10 ची बेरीज करची.

$$\frac{240}{35+25i\sqrt{3}+i\sqrt{300}}$$

300=10^{2}\times 3 गुणकपद काडचें. \sqrt{10^{2}}\sqrt{3} च्या वर्ग मूळाचो गुणाकार म्हूण \sqrt{10^{2}\times 3} च्या वर्गमूळाचो गुणाकार परत बरोवचो. 10^{2} चें वर्गमूळ घेवचें.

$$\frac{240}{35+25i\sqrt{3}+i\times 10\sqrt{3}}$$

35i\sqrt{3} मेळोवंक 25i\sqrt{3} आनी 10i\sqrt{3} एकठांय करचें.

$$\frac{240}{35+35i\sqrt{3}}$$

न्युमरेटर आनी डिनोमिनेटर 35-35i\sqrt{3} न गुणून \frac{240}{35+35i\sqrt{3}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{240\left(35-35i\sqrt{3}\right)}{\left(35+35i\sqrt{3}\right)\left(35-35i\sqrt{3}\right)}$$

विचारांत घेयात \left(35+35i\sqrt{3}\right)\left(35-35i\sqrt{3}\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{240\left(35-35i\sqrt{3}\right)}{35^{2}-\left(35i\sqrt{3}\right)^{2}}$$

1225 मेळोवंक 2 चो 35 पॉवर मेजचो.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(35i\sqrt{3}\right)^{2}}$$

\left(35i\sqrt{3}\right)^{2} विस्तारीत करचो.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(35i\right)^{2}\left(\sqrt{3}\right)^{2}}$$

-1225 मेळोवंक 2 चो 35i पॉवर मेजचो.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(-1225\left(\sqrt{3}\right)^{2}\right)}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(-1225\times 3\right)}$$

-3675 मेळोवंक -1225 आनी 3 गुणचें.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(-3675\right)}$$

3675 मेळोवंक -1 आनी -3675 गुणचें.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225+3675}$$

4900 मेळोवंक 1225 आनी 3675 ची बेरीज करची.

$$\frac{240\left(35-35i\sqrt{3}\right)}{4900}$$

\frac{12}{245}\left(35-35i\sqrt{3}\right) मेळोवंक 240\left(35-35i\sqrt{3}\right) क 4900 न भाग लावचो.

$$\frac{12}{245}\left(35-35i\sqrt{3}\right)$$

35-35i\sqrt{3} न \frac{12}{245} गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{12}{245}\times 35+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

एकोडो अपूर्णांक म्हूण \frac{12}{245}\times 35 स्पश्ट करचें.

$$\frac{12\times 35}{245}+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

420 मेळोवंक 12 आनी 35 गुणचें.

$$\frac{420}{245}+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

35 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{420}{245} उणो करचो.

$$\frac{12}{7}+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

-\frac{12}{7}i मेळोवंक \frac{12}{245} आनी -35i गुणचें.

$$\frac{12}{7}-\frac{12}{7}i\sqrt{3}$$

वास्तवीक भाग

$$240Re(\frac{1}{35\left(1+\sqrt{3}i\right)})$$