Posted by haritha on Friday, June 6, 2014 at 8:44pm.
If a+ib = (root of 1+i) / (root of 1i )then prove a^2 +b^2 =1

math  Steve, Saturday, June 7, 2014 at 6:15am
√(1+i)/√(1i)
= √(1+i)√(1i) / (1i)
= √(1i^2) / (1i)
= √2/(1i)
= √2(1+i) / (1i)(1+i)
= √2(1+i)/2
= 1/√2 + 1/√2 i
a = 1/√2
b = 1/√2
a^2+b^2 = 1/2 + 1/2 = 1

math  Steve, Saturday, June 7, 2014 at 11:59am
or, using de Moivre's rule,
1+i = √2 cis π/4
so √(1+i) = ∜2 cis π/8
1i = √2 cis π/4
so √(1i) = ∜2 cis π/8
√(1+i)/√(1i) = cis π/4
Now the angle doesn't matter, since cos^2+sin^2 = 1
Answer This Question
Related Questions
 maths surds please help and explain  Simplify A.1/root a +2 b.root 18/25 c.root...
 Math  When Synthetically dividing to find a real root out of all Possible Roots...
 Math simplifying mixed radicals  Please help me simplify these following mixed ...
 Math ~CHECK MY ANSWER~  1) Which of these is a rational number? a. Pi b. Square...
 Algebra  Rationalize each expression by building perfect nth root factors for ...
 math  1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. ...
 maths  prove that : 3^3 * 6^2 * root 98 divided by 5 ^2 * cube root 1/25 * 15...
 math  find a and b for the following: 1).(root of 2+root of 3 / 3 root of 2  ...
 math  simplify square 48/square6 square root(48) is the same as sq root (8) x ...
 Math simplifying mixed radicals  Please help me simplify these following mixed ...
More Related Questions