Question

Question 14 Express the following expression in the form of a + ib.

[ (3+i.5^(1/2))(3-i.5^(1/2)) ] / [(3^0.5 + i.2^0.5)(3^0.5 - i.2^0.5) ]

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 104

Answer 1

(3 + i√5)(3-i√5)(√3+i√2)-(√3-i√2)

we know, that
a² - b² = (a - b)(a + b)
use this concept here,

= {(3)² - (i√5)²}/(√3 +i√2 -√3+i√2)
={9 -(i²)5}/2√2i
we know, i² = -1 use this here,

= (9+5)/2√2i
=14/2√2i
multiply i with numerator and denominator
= 14i/2√2i²
= -(7/√2)i
= 0 + (-7/√2)i