Question

$\frac{ - 3}{2(± \frac{3i}{ \sqrt{2} } )}$
Please a detailed explanation !​

Answer 1

Step-by-step explanation:

$\frac{ - 3}{2(± \frac{3i}{ \sqrt{2} } )} = \frac{ - 3}{2±3 \sqrt{2} i} \\ \\ \frac{ - 3}{2 + 3 \sqrt{2} i} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{ - 3}{2 - 3 \sqrt{2} i} \\ \\ \frac{ - 3}{2 + 3 \sqrt{2} i} \times \frac{2 - 3\sqrt{2}i }{2 - 3\sqrt{2}i} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{ - 3}{2 - 3 \sqrt{2} i} \times \frac{2 + 3\sqrt{2}i}{2 + 3\sqrt{2}i} \\ \\ \frac{ - 6 + 9 \sqrt{2} i}{ {(2)}^{2} - {(3 \sqrt{2} i)}^{2}} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{- 6 - 9 \sqrt{2} i}{ {(2)}^{2} - {(3 \sqrt{2} i)}^{2}} \\ \\ \frac{ - 6 + 9 \sqrt{2} i}{ 4 + 18} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{- 6 - 9 \sqrt{2} i}{ 4 + 18} \\ \\ \frac{ 3( - 2 + 3 \sqrt{2} i)}{21} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{ 3( - 2 - 3 \sqrt{2} i)}{21} \\ \\ \frac{ - 2 + 3 \sqrt{2} i}{7} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{ - 2 - 3 \sqrt{2} i}{7} \\ \\ \frac{ - 2 ± 3 \sqrt{2} i}{7} \\ \\ = \frac{ - 2}{7} ± \frac{3 \sqrt{2}i }{7} \\ \\ \color{blue}real \: part = \frac{ - 2}{7} \\ \\ \color{blue}imaginary \: part = ± \frac{3 \sqrt{2} i}{7} \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$