Question

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

Answer 1

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)))`.

Answer 2

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

Step-by-step explanation: