Operations of Complex Numbers (Excluding Division)

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 i² = -1.

Front

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

Back

The sum is (a + c) + (b + d)i.

Front

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

Back

The product is (ac - bd) + (ad + bc)i.

Front

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

Back

The result is 3 + 2i.

Front

What is the result of subtracting (2 - 9i) from (10 + 3i)?

Back

The result is 12 + 12i.

Front

What is the result of multiplying (2i) and (3i)?

Back

The result is -6.

Front

What is the result of adding 3i and 2i?

Back

The result is 5i.

Front

What is the result of subtracting (-2 + 10i) from (10 + 3i)?

Back

The result is 12 - 7i.

Front

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

Back

The conjugate is a - bi.

Front

How do you find the modulus of a complex number a + bi?

Back

The modulus is √(a² + b²).