Simplify, add and subtract 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 complex numbers?

Back

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

Front

How do you subtract complex numbers?

Back

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

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

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

How do you simplify (2 - 4i) + (5 + 7i)?

Back

(2 - 4i) + (5 + 7i) = (2 + 5) + (-4 + 7)i = 7 + 3i.

Front

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

Back

(11 - 7i) - (-3 + 12i) = (11 + 3) + (-7 - 12)i = 14 - 19i.

Front

How do you combine like terms in complex numbers?

Back

Combine like terms by adding or subtracting the real parts and the imaginary parts separately.

Front

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

Back

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

Front

What is the simplified form of 4 + 5i + 6 + 6i?

Back

4 + 5i + 6 + 6i = (4 + 6) + (5 + 6)i = 10 + 11i.