Question

Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is

• A. $(+\sin\theta, +\cos\theta)$
• B. $(\sin\theta, -\cos\theta)$
• C. $(\cos\theta, \sin\theta)$
• D. $(-\cos\theta, \sin\theta)$

Hint:

To find the inverse of a complex number $a + ib$, use $\dfrac{a - ib}{a^2 + b^2}$.

Answer 1

The Correct Option is B

The complex number is $z = \sin\theta + i\cos\theta$
Its inverse is $\dfrac{1}{z} = \dfrac{\bar{z}}{|z|^2} = \dfrac{\sin\theta - i\cos\theta}{1} = \sin\theta - i\cos\theta$
Hence, in ordered pair form: $(\sin\theta, -\cos\theta)$