Imaginary and Complex Numbers Test

Front

What is an imaginary number?

Back

An imaginary number is a 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 a complex number?

Back

A complex number is a number that has a real part and an imaginary part, expressed in the form a + bi, where a is the real part and b is the imaginary part.

Front

What is the formula for multiplying two complex numbers (a + bi)(c + di)?

Back

The formula is (a + bi)(c + di) = ac + adi + bci + bdi^2, which simplifies to (ac - bd) + (ad + bc)i.

Front

What is the result of multiplying (4 - 3i)(-7 - 2i)?

Back

The result is -34 + 13i.

Front

How do you add two complex numbers?

Back

To add two complex numbers, simply add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the sum of (5 + 4i) and (6 - 5i)?

Back

The sum is 11 - i.

Front

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

Back

The result is -2 + 6i.

Front

What is the formula for dividing two complex numbers (a + bi) / (c + di)?

Back

To divide, multiply the numerator and denominator by the conjugate of the denominator: (a + bi)(c - di) / (c + di)(c - di). This simplifies to (ac + bd) + (bc - ad)i / (c^2 + d^2).

Front

Back

Front

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

Back

The conjugate of a complex number a + bi is a - bi.