If z -cos-isin- then- zn-1-zn-2 cos n - zn-1-zn-2ncos n - zn-1-zn-2 insin n -D- zn-1-zn-2n i sin n -

1/z=1/cosθ+isinθ=cosθ isinθ ∴ z^n=(cosθ isinθ)^n=cos nθ+isinnθ and 1/z^n=(cosθ isinθ)^n=cos nθ+isin nθ Hence, z^n+1/z^n=2cos nθ and z^n 1/z^n=2isin nθ ...

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Byju's Answer

Standard XII

Mathematics

Iota

If z =cosθ+is...

Question

If $z = c o s θ + i s i n θ$ , then

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Solution

The correct option is A
$\frac{1}{z} = \frac{1}{c o s θ + i s i n θ} = c o s θ - i s i n θ ∴ z^{n} = (c o s θ - i s i n θ)^{n} = c o s n θ + i s i n n θ a n d \frac{1}{z^{n}} = (c o s θ - i s i n θ)^{n} = c o s n θ + i s i n n θ H e n c e, z^{n} + \frac{1}{z^{n}} = 2 c o s n θ a n d z^{n} - \frac{1}{z^{n}} = 2 i s i n n θ$

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If z=cosθ+isinθ, then

The correct option is A 1z=1cosθ+isinθ=cosθ−isinθ∴zn=(cosθ−isinθ)n=cosnθ+isinnθand 1zn=(cosθ−isinθ)n=cosnθ+isinnθHence, zn+1zn=2cosnθ and zn−1zn=2isinnθ

If $z = c o s θ + i s i n θ$ , then