Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
z=0
Evaluate
∣z∣=z×12i
Multiply the terms
More Steps
Evaluate
z×12i
Use the commutative property to reorder the terms
12zi
Multiply the numbers
12iz
∣z∣=12iz
Rewrite the expression
∣z∣−12iz=0
Substitute a+ib for z
∣a+ib∣−12i(a+ib)=0
Rewrite the expression
∣a+ib∣−12ia+12b=0
Use ∣a+bi∣=a2+b2 to calculate the modulus
a2+b2−12ia+12b=0
Rewrite the expression
(a2+b2+12b)+(−12a)i=0
Rewrite the expression
{a2+b2+12b=0−12a=0
Solve the equation for a
More Steps
Evaluate
−12a=0
Change the signs on both sides of the equation
12a=0
Rewrite the expression
a=0
{a2+b2+12b=0a=0
Substitute the given value of a into the equation a2+b2+12b=0
02+b2+12b=0
Simplify
More Steps
Evaluate
02+b2+12b
Calculate
0+b2+12b
Removing 0 doesn't change the value,so remove it from the expression
b2+12b
Reduce the index of the radical and exponent with nan=a
∣b∣+12b
∣b∣+12b=0
Separate the equation into 2 possible cases
b+12b=0,b≥0−b+12b=0,b<0
Solve the equation
More Steps
Evaluate
b+12b=0
Calculate
More Steps
Evaluate
b+12b
Collect like terms by calculating the sum or difference of their coefficients
(1+12)b
Add the numbers
13b
13b=0
Rewrite the expression
b=0
b=0,b≥0−b+12b=0,b<0
Solve the equation
More Steps
Evaluate
−b+12b=0
Calculate
More Steps
Evaluate
−b+12b
Collect like terms by calculating the sum or difference of their coefficients
(−1+12)b
Add the numbers
11b
11b=0
Rewrite the expression
b=0
b=0,b≥0b=0,b<0
Find the intersection
b=0b=0,b<0
Find the intersection
b=0b∈∅
Find the union
b=0
Calculate
{a=0b=0
Solution
z=0
Show Solution
