Write \\(7-3i\\) in the form \\(a+bi\\) by naming \\(a\\) and \\(b\\).

What property of the imaginary unit \\(i\\) is used to simplify powers of \\(i\\)?

Identify the real part and imaginary coefficient of \\(-5+8i\\).

Rewrite \\(4+i\\sqrt{11}\\) as \\(a+bi\\), then state \\(a\\) and \\(b\\).

Simplify \\(6+4i^2\\) into standard complex form.

Simplify \\(3i^2-2i+9\\) into standard form.

A point in the complex plane has coordinates \\((-2,5)\\). Write the corresponding complex number.

A complex number has real part \\(0\\) and imaginary coefficient \\(-6\\). Write it in standard form and describe its position in the complex plane.

Find \\(a\\) and \\(b\\) if \\(a+bi=12-7i\\).

Find real numbers \\(a\\) and \\(b\\) if \\((a-2)+(b+3)i=5-4i\\).

Explain why \\(x^2+1=0\\) has no real solution but has complex solutions.

Show that \\(2+0i\\) and \\(2\\) represent the same complex number, then state its imaginary coefficient.

Find real \\(p\\) and \\(q\\) if \\((p+q)+(p-q)i=10+2i\\).

Find \\(t\\) if the complex number \\((t^2-9)+(t-3)i\\) is equal to \\(0\\).

For what real values of \\(t\\) is \\((t^2-4)+(t+2)i\\) purely imaginary?

For what real values of \\(t\\) is \\((t-1)+(t^2-1)i\\) a real number?

Find all real \\(t\\) for which \\((t^2-1)+(t^2+t-2)i=0\\).

A learner says \\(\\operatorname{Im}(4-9i)=-9i\\). Diagnose the error and give the correct value.

Prove from standard form that if \\(a+bi=c+di\\), then \\(a=c\\) and \\(b=d\\).

A complex number is both real and purely imaginary. What must it be? Justify using \\(a+bi\\).