Question

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

a. 2 + 5i
b. −6 + i

Answer 1

(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

Explanation:

We have given

(a) 2+5i

We have to represent in polar form

We know that magnitude is given by
`√((real\ part)^2+(imaginary\ part)^2)=√(2^2+5^2)=√(29)`

Argument is given by
`tan^(-1)(imaginary\ part)/(real\ part)=tan^(-1)(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* (\pi )/(180)=0.378\pi`

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

We know that magnitude is given by
`√((real\ part)^2+(imaginary\ part)^2)=√((-6)^2+1^2)=√(37)`

Argument is given by
`tan^(-1)(imaginary\ part)/(real\ part)=tan^(-1)(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* (\pi )/(180)=-0.05255\pi`