MRWC - Chapter 4&5 Summary

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 the square root of -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which is used to extend the real number system to include complex numbers.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi, where a is the real part and b is the imaginary part.

Front

What is the conjugate of -2i + 7?

Back

The conjugate of -2i + 7 is 7 + 2i.

Front

What is the conjugate of -2 + 5i?

Back

The conjugate of -2 + 5i is -2 - 5i.

Front

How do you add two complex numbers?

Back

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

Front

Calculate (5 - 2i) + (-7 + 8i).

Back

(5 - 2i) + (-7 + 8i) = -2 + 6i.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by the formula |a + bi| = √(a² + b²).

Front

How do you find the modulus of -3 + 4i?

Back

The modulus of -3 + 4i is | -3 + 4i | = √((-3)² + (4)²) = √(9 + 16) = √25 = 5.