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

Calculate the conjugate of 3 + 4i.

Back

3 - 4i

Front

What is the result of multiplying two imaginary numbers, i and i?

Back

i * i = i^2 = -1.

Front

Calculate: (2 + 3i) + (4 + 5i).

Back

6 + 8i.

Front

What is the result of subtracting two complex numbers: (5 + 2i) - (3 + 4i)?

Back

2 - 2i.

Front

Calculate: (1 + 2i)(3 - 4i).

Back

11 - 10i.

Front

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

Back

The modulus is given by √(a² + b²).

Front

Calculate the modulus of 3 + 4i.

Back

5 (since √(3² + 4²) = √(9 + 16) = √25 = 5).

Front

What is the real part of the complex number 7 - 2i?

Back

7.