Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(z−1)(z+1)(z2+1)
Evaluate
z4−1
Rewrite the expression in exponential form
(z2)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(z2−1)(z2+1)
Solution
More Steps
Evaluate
z2−1
Rewrite the expression in exponential form
z2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(z−1)(z+1)
(z−1)(z+1)(z2+1)
Show Solution
Find the roots
z1=−1,z2=1
Evaluate
z4−1
To find the roots of the expression,set the expression equal to 0
z4−1=0
Move the constant to the right-hand side and change its sign
z4=0+1
Removing 0 doesn't change the value,so remove it from the expression
z4=1
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±41
Simplify the expression
z=±1
Separate the equation into 2 possible cases
z=1z=−1
Solution
z1=−1,z2=1
Show Solution