Convert to Trigonometric Form -8i

$- 8 i$

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 $a = 0$ and $b = - 8$ .

$| z | = \sqrt{{(- 8)}^{2}}$

Find $| z |$ .

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Raise $- 8$ to the power of $2$ .

$| z | = \sqrt{64}$

Rewrite $64$ as $8^{2}$ .

$| z | = \sqrt{8^{2}}$

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

$| z | = 8$

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

$θ = \arctan (\frac{- 8}{0})$

Since the argument is undefined and $b$ is negative, the angle of the point on the complex plane is $\frac{3 π}{2}$ .

$θ = \frac{3 π}{2}$

Substitute the values of $θ = \frac{3 π}{2}$ and $| z | = 8$ .

$8 (\cos (\frac{3 π}{2}) + i \sin (\frac{3 π}{2}))$

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Name

Name	one billion one hundred ninety-one million seventeen thousand nine hundred thirty-nine

Interesting facts

1191017939 has 4 divisors, whose sum is 1191199224
The reverse of 1191017939 is 9397101911
Previous prime number is 6827

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 41
Digital Root 5

Name

Name	two billion sixty-one million three hundred seventy-seven thousand eight hundred seventy-six

Interesting facts

2061377876 has 16 divisors, whose sum is 4642218540
The reverse of 2061377876 is 6787731602
Previous prime number is 1129

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	one billion five hundred sixty-two million six hundred five thousand five hundred fifty-seven

Interesting facts

1562605557 has 8 divisors, whose sum is 2114570976
The reverse of 1562605557 is 7555062651
Previous prime number is 67

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

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