Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
z∈/R
Alternative Form
No real solution
Evaluate
{z×1=23iz2=1×i
Any expression multiplied by 1 remains the same
{z=23iz2=1×i
Calculate
More Steps
Evaluate
3iz2=1×i
Any expression multiplied by 1 remains the same
3iz2=i
Simplify
z=i
Rewrite the complex number in polar form
More Steps
Evaluate
i
Determine the modulus and the argument of the complex number
r=02+12θ=arctan(01)
Calculate
r=1θ=arctan(01)
Substitute the given values into the formula r(cosθ+isinθ)
1×(cos(2π)+isin(2π))
z=1×(cos(2π)+isin(2π))
Calculate the nth roots of a complex r(cos(θ)+i×sin(θ),using nz=nr(cosnθ+2kπ+isinnθ+2kπ)
z=1×(cos(22π+2kπ)+isin(22π+2kπ))
Simplify
z=cos(22π+2kπ)+isin(22π+2kπ)
Since n=2,substitute k=0,1 into the expression
z1=cos(22π+2×0×π)+isin(22π+2×0×π)z2=cos(22π+2×1×π)+isin(22π+2×1×π)
Calculate
More Steps
Evaluate
22π+2×0×π
Any expression multiplied by 0 equals 0
22π+0
Removing 0 doesn't change the value,so remove it from the expression
22π
Multiply by the reciprocal
2π×21
To multiply the fractions,multiply the numerators and denominators separately
2×2π
Multiply the numbers
4π
z1=cos(4π)+isin(4π)z2=cos(22π+2×1×π)+isin(22π+2×1×π)
Calculate
More Steps
Evaluate
22π+2×1×π
Multiply the terms
22π+2π
Calculate
225π
Multiply by the reciprocal
25π×21
To multiply the fractions,multiply the numerators and denominators separately
2×25π
Multiply the numbers
45π
z1=cos(4π)+isin(4π)z2=cos(45π)+isin(45π)
Calculate
z1=22+22i∪z2=−22−22i
{z=2z1=22+22i∪z2=−22−22i
Solution
z∈/R
Alternative Form
No real solution
Show Solution
