# Simplify ( square root of fourteen(cos(one hundred twenty) plus i times sin(one hundred twenty))) to the power of four

Simplify ( square root of 14(cos(120)+i*sin(120)))^4
Clarify each term.
Use the reference angle by calculating the angle with equivalent triginometric values in the Initially quadrant. Should be rewritten the expression as a negative one since cosine is negative in the 2nd 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 .
Clarify terms.
Use the distributive law.
First, multiply .
Combine and .
Multiply by .
Apply the binomial theorem.
Simplify terms.
Simplify each term.
Apply the power rule for exponent distribution.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
Clarify the numerator.
Rewrite as .
Rewrite as .
Use the power rule when multiplying the exponents, .
Combine and .
The common factor should be canceled of and .
Factor out of .
The common factors should be canceled.
Factor out of .
Cancel the common factor.
Reformulate the expression.
First, divide by .
Raise to the power of .
Raise to the power of .
The common factor should be canceled and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
The common factor should be canceled.
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 .
Withdraw terms 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.
Put 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.
First, multiply by .
The common factor should be canceled 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 .
Solve 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 .
The common factor should be canceled 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 .
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 .
The common factor should be canceled 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 .
The common factor should be canceled 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.
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.
Add fractions with the same denominators.
Clarify the expression.
Subtract from .
Divide by .
Shift the factors of .