Question

What is the standard form of (1+2√-3)/(1+√-3)

Answer 1

1.75+0.43301270i
hope this helped and let me know if i was right plz

Answer 2

Answer:

$\frac{7}{4} +\frac{3}{4} i$

Step-by-step explanation:

$(1+2\sqrt{-3} )/(1+\sqrt{-3})$

To remove the negative sign from square root use 'i'

square root (-1) is 'i'

$\frac{1+2\sqrt{3}i}{1+\sqrt{3}i}$

Multiply top and bottom by conjugate of $(1+\sqrt{3}i)$

Conjugate of $(1+\sqrt{3}i)$ is $(1-\sqrt{3}i)$

Multiply it at the top and bottom

$\frac{1+2\sqrt{3}i}{1+\sqrt{3}i} \cdot \frac{1-\sqrt{3}i}{1-\sqrt{3}i}$

Multiply numerator and denominator using FOIL method

$\frac{1-\sqrt{3}i+2\sqrt{3}i-3i^2}{1+3}$

the value of i^2 is -1

$\frac{1+\sqrt{3}i-6(-1)}{4}$

$\frac{1+\sqrt{3}i+6}{4}$

$\frac{7+\sqrt{3}i}{4}$

$\frac{7}{4} +\frac{3}{4} i$