Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi, where a and b are real numbers.

Front

Find the conjugate of: -4 − 8i

Back

-4 + 8i

Front

What is the product of two complex conjugates (a + bi)(a - bi)?

Back

The product is a² + b², which is a real number.

Front

Calculate (multiply): (4 + 3i)(4 − 3i)

Back

25

Front

What is the result of multiplying a complex number by 'i'?

Back

Multiplying a complex number by 'i' rotates it 90 degrees counterclockwise in the complex plane.

Front

Calculate: 6i (-5 + 10i)

Back

-30i + 60i²

Front

What is the value of i²?

Back

i² = -1.

Front

Calculate (multiply): (1 − 2i)(6 + 5i)

Back

16 − 7i

Front

What is the sum of two complex numbers?

Back

The sum of two complex numbers a + bi and c + di is (a + c) + (b + d)i.