Value of (( cos θ+i sin θ)4/( cos θ-i sin θ)3) is

Question

Value of (( cos θ+i sin θ)4/( cos θ-i sin θ)3) is (A) cos 5 θ+i sin 5 θ (B) cos 7 θ+i sin 7 θ (C) cos 4 θ+ i sin 4 θ (D) cos θ+i sin θ

Tardigrade Admin · Accepted Answer

((cos θ+i sin θ)4/(cos θ-i sin θ)3) =(cos θ+i sin θ)4(cos θ-i sin θ)-3 =(cos 4 θ+ i sin 4 θ) cos (-θ)+ i sin (-θ) -3 =(cos 4 θ+ i sin 4 θ) cos (-3)(-θ)+ i sin (-3)(-θ) =(cos 4 θ+ i sin 4 θ) cos 3 θ+ i sin 3 θ =cos 4 θ cos 3 θ-sin 4 θ sin 3 θ + i (sin 4 θ cos 3 θ+sin 3 θ cos 4 θ) =cos (4 θ+3 θ)+ i sin (4 θ+3 θ)=cos 7 θ+ i sin 7 θ

Q. Value of $\frac{( c o s θ + i s i n θ ) ^{4}}{( c o s θ - i s i n θ ) ^{3}}$ is

$cos 5 θ + i s in 5 θ$

$cos 7 θ + i s in 7 θ$

$cos 4 θ + i s in 4 θ$

$cos θ + i s in θ$

Q. Value of (cosθ−isinθ)3(cosθ+isinθ)4​ is

cos5θ+isin5θ

cos7θ+isin7θ

cos4θ+isin4θ

cosθ+isinθ

Q. Value of $\frac{( c o s θ + i s i n θ ) ^{4}}{( c o s θ - i s i n θ ) ^{3}}$ is

$cos 5 θ + i s in 5 θ$

$cos 7 θ + i s in 7 θ$

$cos 4 θ + i s in 4 θ$

$cos θ + i s in θ$