Question

show that this is real​

Answer 1

Step-by-step explanation:

simply calculate the value of

simply calculate the value of {[(√7+i√3)/(√7-i√3)]+[(√7-i√3)/(√7+i√3)]} by taking lcm

{[(√7+i√3)/(√7-i√3)]+[(√7-i√3)/(√7+i√3)]}

={(√7+i√3)(√7+i√3)+(√7-i√3)(√7-i√3)} /{(√7-i√3)(√7+i√3)}

={(√7+i√3)²+(√7-i√3)²}/(√7)²-(i√3)²

use (a+b)²= a²+2ab+b² and (a-b)²=a²-2ab+b² in a numerator and use (a+b)(a-b) = a²-b² in a denominator side :

={7+2√7x(√3i)+(i√3)²+7-2√7x(√3i)+(i√3)²}/ {(√7)²-(i√3)²}

={7+(-1)(3)+7+(-1)(3)}/{(7)-(-1)(3)}

={7-3 +7-3}/(7+3) = (14-6)/10 = 4/5

So the 4/5 is a real number

Hence {[(√7+i√3)/(√7-i√3)]+[(√7-i√3)/(√7+i√3)]} is a real number