Question

Need some help, kinda stuck

Answer 1

Answer:

7/4

Step-by-step explanation:

$\displaystyle\frac{2 + \sqrt{ - 3} }{2} ( \frac{2 - \sqrt{ - 3} }{2} )~~~~~~$

Evaluate.

Solution:

Rewrite it as,

• $\displaystyle\frac{2 + \sqrt{ - 1 } \sqrt{ 3} }{2} ( \frac{2 - \sqrt{ - 1} \sqrt{3} }{2} )$
• $\displaystyle\frac{2 + i\sqrt{ 3} }{2} ( \frac{2 - i\sqrt{ 3} }{2} )~~~~~~$

Multiplying them,

• $\displaystyle\frac{(2 + i\sqrt{ 3})\times(2 - i \sqrt{3}) }{2 \times 2}$

• $\displaystyle\frac{(2 + i\sqrt{ 3})\times(2 - i \sqrt{3}) }{4}$

Applying Distributive property,

• $\displaystyle\frac{2(2 + i\sqrt{ 3}) + \: i \sqrt{3} (2 - i \sqrt{3}) }{4}$

• $\cfrac{2 \times 2 + 2( - i \sqrt{3} ) + i \sqrt{3}(2 - i \sqrt{3} ) }{4}$

• $\cfrac{2 \times 2 + 2( - i \sqrt{3}) + i \sqrt{3} \times 2 + i \sqrt{3} ( - i \sqrt{3}) }{4}$

Combining each terms,

• $\cfrac{4 - 2i \sqrt{3} + 2i \sqrt{3} + 3}{4}$
• $\cfrac{ - 2i \sqrt{3} + 2i \sqrt{3} + 7 }{4}$
• $\boxed{\cfrac{ 7}{4} }$

Last Choice is accurate.