Complex Numbers and Quadratic Equations

Front

What is a complex number?

Back

A complex number is a number of the form a + ib, where a and b are real numbers.

Front

What does 'i' represent in complex numbers?

Back

The symbol 'i' represents the square root of -1.

Front

What is the real part of a complex number z = a + ib?

Back

The real part is denoted by Re z and is equal to 'a'.

Front

What is the imaginary part of a complex number z = a + ib?

Back

The imaginary part is denoted by Im z and is equal to 'b'.

Front

How do you add two complex numbers z1 = a + ib and z2 = c + id?

Back

The sum is given by z1 + z2 = (a + c) + i(b + d).

Front

What is the closure law for addition of complex numbers?

Back

The sum of two complex numbers is a complex number.

Front

What is the commutative law for addition of complex numbers?

Back

For any two complex numbers z1 and z2, z1 + z2 = z2 + z1.

Front

What is the associative law for addition of complex numbers?

Back

For any three complex numbers z1, z2, z3, (z1 + z2) + z3 = z1 + (z2 + z3).

Front

What is the additive identity in complex numbers?

Back

The additive identity is the complex number 0 + i0, denoted as 0.

Front

What is the additive inverse of a complex number z = a + ib?

Back

The additive inverse is -a - ib.