Practice 5.5

Front

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

Back

The sum is -2 + 6i.

Front

Simplify (1+3i) + (7-2i).

Back

The result is 8 + i.

Front

What is the product of (1-3i)(2+5i)?

Back

The product is 17 - i.

Front

Simplify (2 - 5i)(4 + i).

Back

The result is 13 - 18i.

Front

What is the result of (10-6i) - (2+3i)?

Back

The result is 8 - 9i.

Front

Define 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.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

How do you add complex numbers?

Back

To add complex numbers, add their real parts and their imaginary parts separately.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately.

Front

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

Back

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