Trigonometry Examples

Find All Complex Solutions x^4=4
Step 1
Subtract from both sides of the equation.
Step 2
Factor the left side of the equation.
Tap for more steps...
Step 2.1
Rewrite as .
Step 2.2
Rewrite as .
Step 2.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4
Set equal to and solve for .
Tap for more steps...
Step 4.1
Set equal to .
Step 4.2
Solve for .
Tap for more steps...
Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.2.3
Simplify .
Tap for more steps...
Step 4.2.3.1
Rewrite as .
Step 4.2.3.2
Rewrite as .
Step 4.2.3.3
Rewrite as .
Step 4.2.4
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
Step 4.2.4.1
First, use the positive value of the to find the first solution.
Step 4.2.4.2
Next, use the negative value of the to find the second solution.
Step 4.2.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
Set equal to and solve for .
Tap for more steps...
Step 5.1
Set equal to .
Step 5.2
Solve for .
Tap for more steps...
Step 5.2.1
Add to both sides of the equation.
Step 5.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.2.3
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
Step 5.2.3.1
First, use the positive value of the to find the first solution.
Step 5.2.3.2
Next, use the negative value of the to find the second solution.
Step 5.2.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 6
The final solution is all the values that make true.