Question

Let the point P represent the non-zero complex number $Z=x+i y$ and directed line segment $O P=r$ and it is inclined with positive direction of $X$ - axis at an angle $\theta$, then
Complex number $Z=x+i y$ in terms of $r$ and $\theta$ can be written as

• A. $Z=r(\cos \theta+i \sin \theta)$
• B. $Z=r(\sin \theta+i \cos \theta)$
• C. $Z=r(\sin \theta-i \cos \theta)$
• D. None of these

Answer 1

Answer: (A)

Let complex number $z=x+i y$
$\because O P=r, \angle P O X=\theta x=r \cos \theta ; y=r \sin \theta .$
Hence, $z=r(\cos \theta+i \sin \theta)$