If a-ib- x-i 2 2x 2 -1- prove that a 2 - b 2 - x 2 -1 2 2x2-1 2-

a+ib=( x+i ) #160;^ 2 / 2x ^ 2 +1 #160; = x ^ 2 + i ^ 2 +2xi / 2 x ^ 2 +1 #160; = x ^ 2 1+2xi / 2 x ^ 2 +1 #160; = x ^ 2 1 / 2 ...

If a+ib= x+...

Question

If $a + i b = \frac{{(x + i)}^{2}}{{2 x}^{2} + 1}$ , prove that $a^{2} + b^{2} = \frac{{(x^{2} + 1)}^{2}}{{(2 x^{2} + 1)}^{2}}$ .

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If $a + i b = \frac{(x + i)^{2}}{(2 x^{2} + 1)}$ , prove that $a^{2} + b^{2} = \frac{(x^{2} + 1)^{2}}{(2 x^{2} + 1)^{2}}$

x + i y = \sqrt{\frac{a + i b}{c + i d}}

(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

(x + i y) = \sqrt{\frac{a + i b}{c + i d}}

(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

(a + i b) = \frac{1 + i}{1 - i}

(a^{2} + b^{2}) = 1

a + i b = \frac{p + i}{2 q - i}

a^{2} + b^{2} = \frac{(p^{2} + 1)}{4 q^{2} + 1}