Convert to Trigonometric Form 3+4i

$3 + 4 i$

This is the trigonometric form of a complex number where $| z |$ is the modulus and $θ$ is the angle created on the complex plane.

$z = a + b i = | z | (\cos (θ) + i \sin (θ))$

The modulus of a complex number is the distance from the origin on the complex plane.

$| z | = \sqrt{a^{2} + b^{2}}$ where $z = a + b i$

Substitute the actual values of $a = 3$ and $b = 4$ .

$| z | = \sqrt{4^{2} + 3^{2}}$

Find $| z |$ .

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Raise $4$ to the power of $2$ .

$| z | = \sqrt{16 + 3^{2}}$

Raise $3$ to the power of $2$ .

$| z | = \sqrt{16 + 9}$

Add $16$ and $9$ .

$| z | = \sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$| z | = \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$| z | = 5$

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

$θ = \arctan (\frac{4}{3})$

Since inverse tangent of $\frac{4}{3}$ produces an angle in the first quadrant, the value of the angle is $0.92729521$ .

$θ = 0.92729521$

Substitute the values of $θ = 0.92729521$ and $| z | = 5$ .

$5 (\cos (0.92729521) + i \sin (0.92729521))$

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Name

Name	nine hundred four million five hundred eighty-seven thousand seven hundred forty-five

Interesting facts

904587745 has 4 divisors, whose sum is 1085505300
The reverse of 904587745 is 547785409
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 49
Digital Root 4

Name

Name	one hundred four million twenty-one thousand three hundred eight

Interesting facts

104021308 has 8 divisors, whose sum is 234047952
The reverse of 104021308 is 803120401
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 19
Digital Root 1

Name

Name	one billion three hundred thirty-six million five hundred twenty-nine thousand five hundred eighty-three

Interesting facts

1336529583 has 32 divisors, whose sum is 2461209600
The reverse of 1336529583 is 3859256331
Previous prime number is 877

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

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