Question

For $z=x+iy$, where $x,y\in R$ and $i=\sqrt{-1}$, what is the polar form of representation?

• A. $\sqrt{x^2+y^2}[cos\theta -isin\theta ]$
• B. $\sqrt{x^2-y^2}[cos\theta -isin\theta ]$
• C. $\sqrt{x^2+y^2}[cos\theta +isin\theta ]$
• D. $\sqrt{x^2–y^2}[cos\theta +isin\theta ]$

Answer 1

The correct option is C

$\sqrt{x^2+y^2}[cos\theta +isin\theta ]$

Given,
$z=x+iy$, where $x,y\in R$ and $i=\sqrt{-1}$

$x=OPcos\theta$

$y=OPsin\theta$

$OP=\sqrt{x^2+y^2}$ (hypotenuse in $△$ POM)

$\therefore z=OPcos\theta +iOPsin\theta$

$=OP(cos\theta +isin\theta$)

$=\sqrt{x^2+y^2}[cos\theta +isin\theta ]$