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Write the complex number into polar form
z = 1 + sqrt 3i

Write the complex number into polar form z = 1 + sqrt 3i-example-1
User Tom Sabel
by
8.1k points

2 Answers

6 votes

Final answer:

The complex number
1 + √(3)i in polar form is
2(cos((\pi)/(3)) + i sin((\pi)/(3))).

Step-by-step explanation:

To write the given complex number in polar form, we first need to express the complex number as

z = a + bi,

where

a is the real part and

bi is the imaginary part.

In this case, we have
z = 1 + √(3)i.

The polar form of a complex number is represented as r(cos(θ) + i sin(θ)),

where

r is the magnitude (modulus) of the complex number and

θ is the argument (angle).

To find r, we calculate the magnitude of the complex number using the formula


r = √(a^2 + b^2)

In this case,
r = \sqrt{1^2 + (√(3))^2} = 2.

To find θ, we use the arctangent function (tan^-1(b/a)) to find the angle.

Since a = 1 and
b = √(3)

θ
= tan^-1(√(3)/1),

which gives us

θ =
(\pi)/(3)

So, the polar form of the complex number
z = 1 + √(3)i is
z = 2(cos((\pi)/(3)) + i sin((\pi)/(3))).

User Nhat Dinh
by
8.3k points
3 votes

Answer:

the polar form of z = 1 + √3i is 2(cos(π/3) + i * sin(π/3)).

Step-by-step explanation:

User Galethil
by
8.5k points

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