Complex Number Practice

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, defined as i = √-1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √-1.

Front

What is the conjugate of a complex number?

Back

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

Front

How do you multiply two complex numbers?

Back

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

Front

What is the product of (2i)(3i)?

Back

The product is -6.

Front

What is the product of a complex number and its conjugate?

Back

The product of a complex number a + bi and its conjugate a - bi is a^2 + b^2.

Front

Find the product of 5 + i and its conjugate.

Back

The product is 26.

Front

How do you simplify the square root of a negative number?

Back

To simplify the square root of a negative number, factor out -1: √-x = i√x.

Front

What is √-25?

Back

The result is 5i.

Front

What is the complex conjugate of 4 - 3i?

Back

The complex conjugate is 4 + 3i.