Complex Numbers Review

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i^2 = -1.

Front

How do you simplify the expression 2i - 7i + 10?

Back

The expression simplifies to -5i + 10.

Front

What is the result of multiplying (2i)(3i)?

Back

The result is -6, since (2i)(3i) = 6i^2 = 6(-1) = -6.

Front

What is the product of (-3i)(4i)(-5i)?

Back

The product is -60i.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

How do you add complex numbers?

Back

To add complex numbers, combine their real parts and their imaginary parts separately.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately.

Front

What is the conjugate of a complex number a + bi?

Back

The conjugate of a complex number a + bi is a - bi.

Front

How do you multiply complex numbers in the form (a + bi)(c + di)?

Back

To multiply complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2, and simplify using i^2 = -1.