If c-i-c-i - a-ib- where a-b-c are real- then a2 - b2 -

c+i/c i = a+ib .........(i) ∴ c i/c+i = a ib .........(ii) Multiplying (i) and (ii), we get c^2+1/c^2+1 = a^2 + b^2 ⇒ a^2 + b^2 =1. ...

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Algebra of Complex Numbers

If c+i/c-i = ...

Question

If $\frac{c + i}{c - i}$ = a+ib, where a,b,c are real, then $a^{2} + b^{2}$ =

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-1

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$c^{2}$

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$- c^{2}$

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a + i b = \frac{c + i}{c - i}

c

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

\frac{b}{a} = \frac{2 c}{c^{2} - 1}

If $\frac{c + i}{c - i}$ = a+ib, where a,b,c are real, then $a^{2} + b^{2}$ =

a + i b = \frac{c + i}{c - i}

c

a, b, c

d

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

A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}],

i^{2} = - 1,

A^{- 1} =

a, b, c

d

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

I f A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}]

A^{- 1} =

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