Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

12,391 questions

17,133 answers

1,424 comments

21,754 users

Write the complex number 3 - 4i in polar form. Please show all work

+2 votes
complex number
asked Dec 25, 2012 in PRECALCULUS by dkinz Apprentice

1 Answer

0 votes

The polar form of a complex number z = a + bi is z = r (cos θ + i sin θ), where r = | z | = √(a2 + b2), a = r cos θ, and b = r sin θ, and θ = tan- 1(b / a) for a > 0 or θ = tan- 1(b / a) + π or θ = tan- 1(b / a) + 180o for a < 0.

The complex number is z = 3 - 4i.

The polar form of a complex number z = a + bi is z = r (cos θ + i sin θ).

Here a = 3 > 0 and b = - 4.

So, first find the absolute value of r .

r = | z | = √(a 2 + b 2)

            = √[ (3)2 + (- 4)2 ]

            = √[ 9 + 16 ]

            = √[ 25 ]

            = 5.

Now find the argument θ.

Since a = 3 > 0, use the formula θ = tan- 1(b / a).

θ = tan- 1[ - 4/(3) ]

θ ≅ 53.13o

Note that here θ is measured in degrees.

Therefore, the polar form of 3 - 4i is about 5[ cos(53.13o) + i sin(53.13o) ].

answered Jun 21, 2014 by lilly Expert

The value of θ = tan- 1[ - 4/(3) ] = - tan- 1[4/(3)] ≅ - 53.13o.

Therefore, the polar form of 3 - 4i is about 5[ cos(- 53.13o) + i sin(- 53.13o) ] = 5[ cos(53.13o) - i sin(53.13o) ].

Related questions

asked Jul 7, 2016 in PRECALCULUS by anonymous
asked Jan 26, 2015 in PRECALCULUS by anonymous
...