Question

Expres each complex number in polar form. State the arguments in radians rounded to the nearest thousandth.

Answer 1

Answer:

(a) In polar form complex number will be $5.3851\angle 68.1985^{\circ}$ and in radian argument is 0.378π

(b) $6.0827\angle -9.46^{\circ}$

angle will be 0.05255π

Step-by-step explanation:

We have given

(a) 2+5i

We have to represent in polar form

We know that magnitude is given by $\sqrt{(real\ part)^2+(imaginary\ part)^2}=\sqrt{2^2+5^2}=\sqrt{29}$

Argument is given by $tan^{-1}\frac{imaginary\ part}{real\ part}=tan^{-1}\frac{5}{2}=68.198$

So in polar form complex number will be $5.3851\angle 68.1985^{\circ}$

In radian argument will be $68.1985\times \frac{\pi }{180}=0.378\pi$

(b) We have given complex number $-6+i$

We know that magnitude is given by $\sqrt{(real\ part)^2+(imaginary\ part)^2}=\sqrt{(-6)^2+1^2}=\sqrt{37}$

Argument is given by $tan^{-1}\frac{imaginary\ part}{real\ part}=tan^{-1}\frac{1}{-6}=-9.46$

So in polar form complex number will be $6.0827\angle -9.46^{\circ}$

In radian argument will be $-9.46\times \frac{\pi }{180}=-0.05255\pi$