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 i² = -1.

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

How do you subtract two complex numbers?

Back

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

Front

What is the result of (7 + 2i) - (-12 - 4i)?

Back

19 + 6i.

Front

What is the result of (2 - 4i) + (5 + 7i)?

Back

7 + 3i.

Front

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

Back

-2 + 6i.

Front

How do you simplify √-23?

Back

i√23.

Front

What is the result of (10 + 15i) - (48 - 30i)?

Back

-38 + 45i.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i² = -1.

Front

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

Back

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