Operations on Complex Numbers

Front

What is the simplified form of (11 - 7i) - (-3 + 12i)?

Back

14 - 19i

Front

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

Back

55 - 48i

Front

What is the value of i²?

Back

-1

Front

What is the square root of -75?

Back

5i√3

Front

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

Back

7/10 + 11/10 i

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.

Front

What is the imaginary unit i?

Back

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

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

Front

What is the product of two complex numbers (a + bi)(c + di)?

Back

The product is ac + adi + bci + bdi², which simplifies to (ac - bd) + (ad + bc)i.