If c + i c − i = a+ib, where a,b,c are real, then a 2 + b 2 = Options: A . &nbsp1 B . &nbsp-1 C . &nbspc2 D . &nbsp−c2

Answer: Option A : A 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 .

If c+ic−i = a+ib, where a,b,c are real, then a2+b2 =

Question

\frac{c + i}{c - i}

= a+ib, where a,b,c are real, then

a^{2} + b^{2}

Options:

A . 1

B . -1

C . c2

D . −c2

Answer: Option A
:
A

\frac{c + i}{c - i}

= a+ib .........(i)
∴

\frac{c - i}{c + i}

= a-ib .........(ii)
Multiplying (i) and (ii), we get

\frac{c^{2} + 1}{c^{2} + 1} = a^{2} + b^{2} \Rightarrow a^{2} + b^{2} = 1

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