# Simplify ( square root of 14(cos(120)+i*sin(120)))^4

Simplify ( square root of 14(cos(120)+i*sin(120)))^4
Simplify each term.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
The exact value of is .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Simplify terms.
Apply the distributive property.
Combine and .
Multiply .
Combine and .
Combine using the product rule for radicals.
Multiply by .
Use the Binomial Theorem.
Simplify terms.
Simplify each term.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
Simplify the numerator.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Raise to the power of .
Raise to the power of .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Simplify the numerator.
Rewrite as .
Raise to the power of .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Raise to the power of .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Multiply .
Combine and .
Combine using the product rule for radicals.
Multiply by .
Combine and .
Simplify the numerator.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Move to the left of .
Multiply by .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Raise to the power of .
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Multiply by .
Divide by .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the numerator.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Rewrite as .
Raise to the power of .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Multiply .
Multiply by .
Combine and .
Multiply by .
Move the negative in front of the fraction.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the numerator.
Rewrite as .
Raise to the power of .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Factor out .
Rewrite as .
Rewrite as .
Combine exponents.
Factor out negative.
Multiply by .
Raise to the power of .
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Combine using the product rule for radicals.
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the numerator.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Raise to the power of .
Rewrite as .
Rewrite as .
Rewrite as .
Raise to the power of .
Raise to the power of .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify terms.
Combine fractions with similar denominators.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine fractions with similar denominators.
Simplify the expression.
Subtract from .
Divide by .
Reorder the factors of .
Reorder and .
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### Name

Name one billion six hundred fifty-two million four hundred twenty-three thousand six hundred sixty-six

### Interesting facts

• 1652423666 has 4 divisors, whose sum is 2478635502
• The reverse of 1652423666 is 6663242561
• Previous prime number is 2

### Basic properties

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

### Name

Name one billion six hundred ninety-nine million four hundred fifty-one thousand eight hundred one

### Interesting facts

• 1699451801 has 4 divisors, whose sum is 1799419572
• The reverse of 1699451801 is 1081549961
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 44
• Digital Root 8

### Name

Name two billion sixty-seven million nine hundred twenty-five thousand nine hundred twenty-one

### Interesting facts

• 2067925921 has 4 divisors, whose sum is 2068029844
• The reverse of 2067925921 is 1295297602
• Previous prime number is 26821

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 43
• Digital Root 7