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

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

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

Options:

A . 1

B . -1

C .

c^{2}

D .

- c^{2}

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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