Question
Solve the equation
Solve for n
n=0
Evaluate
∣zn∣=∣z∣n
Move the expression to the left side
∣zn∣−∣z∣n=0
Separate the equation into 2 possible cases
zn−∣z∣n=0,zn≥0−zn−∣z∣n=0,zn<0
Solve the equation
More Steps
Evaluate
zn−∣z∣n=0
Rewrite the expression
−∣z∣n=−zn
Multiply both sides
−(−1)∣z∣n=−(−1)zn
Calculate
∣z∣n=zn
Take the logarithm of both sides
log∣z∣(∣z∣n)=log∣z∣(zn)
Evaluate the logarithm
n=nlog∣z∣(z)
Calculate
n=log∣z∣(z)×n
Add or subtract both sides
n−log∣z∣(z)×n=0
Collect like terms by calculating the sum or difference of their coefficients
(1−log∣z∣(z))n=0
Rewrite the expression
n=0
n=0,zn≥0−zn−∣z∣n=0,zn<0
Solve the inequality
n=0,n∈R−zn−∣z∣n=0,zn<0
Solve the equation
More Steps
Evaluate
−zn−∣z∣n=0
Rewrite the expression
−∣z∣n=zn
Multiply both sides
−(−1)∣z∣n=−1×zn
Calculate
∣z∣n=−zn
Calculate
n∈∅
n=0,n∈Rn∈∅,zn<0
Solve the inequality
n=0,n∈Rn∈∅,n∈∅
Find the intersection
n=0n∈∅,n∈∅
Find the intersection
n=0n∈∅
Solution
n=0
Show Solution