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Proof by mathematical induction

If a+i b=x+i2...

Question

If a + ib =, prove that a² + b² =

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Solution

On comparing real and imaginary parts, we obtain

Hence, proved.

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Similar questions

a + i b = \frac{{(x + i)}^{2}}{{2 x}^{2} + 1}

a^{2} + b^{2} = \frac{{(x^{2} + 1)}^{2}}{{(2 x^{2} + 1)}^{2}}

a + i b = \frac{x + i y}{x - i y}

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

\frac{b}{a} = \frac{2 x y}{x^{2} - y^{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}}

, then prove that

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

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

, then prove that

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

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