# 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 seven hundred sixty-five million seven hundred forty-three thousand five hundred twenty-one

### Interesting facts

• 1765743521 has 4 divisors, whose sum is 1765851312
• The reverse of 1765743521 is 1253475671
• Previous prime number is 20147

### Basic properties

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

### Name

Name nine hundred twenty-six million seven hundred twenty-eight thousand eight hundred thirty

### Interesting facts

• 926728830 has 16 divisors, whose sum is 1729894320
• The reverse of 926728830 is 038827629
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 45
• Digital Root 9

### Name

Name six hundred nine million one hundred forty-eight thousand two hundred eight

### Interesting facts

• 609148208 has 128 divisors, whose sum is 3290706000
• The reverse of 609148208 is 802841906
• Previous prime number is 73

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2