Multiplying Complex Numbers

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 the square root of -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi². Since i² = -1, this simplifies to (ac - bd) + (ad + bc)i.

Front

What is the result of (1 - 3i)(2 + 5i)?

Back

The result is 17 - i.

Front

What is the simplified form of (8 - 3i)²?

Back

The simplified form is 55 - 48i.

Front

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

Back

The product is 48i.

Front

How do you simplify (3 + 8i)(-2 - i)?

Back

The simplified form is 2 - 19i.

Front

What is the result of (-3 - i)(6 - i)?

Back

The result is -19 - 3i.

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 find the modulus of a complex number a + bi?

Back

The modulus of a complex number a + bi is given by √(a² + b²).