Complex Numbers and Radicals

Front

Define 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 i² = -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i² = -1.

Front

Simplify √-16.

Back

4i.

Front

What is the result of (2 + 3i) + (4 - 5i)?

Back

6 - 2i.

Front

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

Back

11 - 5i.

Front

What is the modulus of the complex number 3 + 4i?

Back

5, calculated as √(3² + 4²).

Front

Simplify √(25).

Back

5.

Front

What is the conjugate of the complex number 5 + 2i?

Back

5 - 2i.

Front

Multiply: (4 - 3i)(-7 - 2i).

Back

-34 + 13i.

Front

What is the result of (5 - 2i) + (-7 + 8i)?

Back

-2 + 6i.