Question

2+√-3/4+√-3 write in a+ib form​

Answer 1

$\frac{2 + \sqrt{ - 3} }{4 \sqrt{ - 3} }$

So , we know that √-1 = i

$\frac{2 + i \sqrt{3} }{4 + i \sqrt{3} }$

Now rationalising

$\frac{2 + i \sqrt{3} }{4 + i \sqrt{3} } \times \frac{4 - i \sqrt{3} }{4 - i \sqrt{3} }$

$\frac{8 + 3 + i4 \sqrt{3} - i2 \sqrt{3} }{( {4)}^{2} - ( {i \sqrt{3)} }^{2} }$

$\frac{11 + \sqrt{3} i(4 - 2)}{( {4)}^{2} - ( { \sqrt{3}i) }^{2} }$

$\frac{11 + i(2 \sqrt{3)} }{19}$

Now comparing above equation with a+ib form

$\frac{11 + i2 \sqrt{3} }{19} = a + ib$

a = 11/19

b = 2√3/19