If z=1+2i is a root of the equation z^2 = az+ b find the values of a and b
I have no idea how to answer this, but I'm sure it's pretty simple.
Is it assumed that a and b are real numbers, or can they be imaginary? I don't think this can be solved in the latter case. In the former case, what other number is a root? What factors would that imply?If z=1+2i is a root of the equation z^2 = az+ b find the values of a and b
I have no idea how to answer this, but I'm sure it's pretty simple.
Thanks in advance!
Standard form for complex number z is a+bi.If z=1+2i is a root of the equation z^2 = az+ b find the values of a and b
No, mention of z does not implicitly define a and b as its parts; you can define any variables you want for those parts, such as x and y. There is nothing wrong in using a and b for something else in the problem. They did not already have definitions.Standard form for complex number z is a+bi.
If you have confusion about why a=1 and b=2 do not work, then you should be forgiven because they have written this exercise so that a and b mean different values in the equation than they do in the given root. Parameters should not change value within a single exercise, so they must want people to ignore standard form for z.
In your work, you implicitly assumed that a and b in the problem are real numbers; that is true of the real and imaginary parts, but not necessarily true of variables in a problem in the context of complex numbers.Imaginary number on each side must be same.
I also think so. In my idea the equation is basic quadratic, the variable is z and the unknown coefficients (a and b) are real numbers.I'm sure it's pretty simple.
Lets be sure of the question. Given that [imath]1+2i[/imath] is a root of [imath]z^2=az+b[/imath][imath]~,~\{a,b\} \subseteq \Re[/imath] THENIf z=1+2i is a root of the equation z^2 = az+ b find the values of a and b
I have no idea how to answer this, but I'm sure it's pretty simple.