adding subtracting multiplying and dividing complex numbers

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

How do you add two complex numbers?

Back

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

Front

How do you subtract two complex numbers?

Back

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

Front

What is the product of two complex numbers?

Back

The product of two complex numbers (a + bi) and (c + di) is given by (ac - bd) + (ad + bc)i.

Front

How do you divide two complex numbers?

Back

To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, to divide (a + bi) by (c + di), multiply by (c - di)/(c - di).

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by √(a² + b²). It represents the distance of the complex number from the origin in the complex plane.

Front

How do you represent complex numbers graphically?

Back

Complex numbers can be represented graphically on the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

Front

What is the significance of the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1. It allows for the extension of the real number system to include solutions to equations that do not have real solutions.

Front

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

Back

The result is -2 + 6i.