A2TH Imaginary Numbers

Front

What is the conjugate of a complex number?

Back

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

Front

Find the conjugate of: 5 + 7i

Back

5 − 7i

Front

What is the sum of i and 6i?

Back

7i

Front

What is the value of i^2?

Back

-1

Front

What is the result of multiplying a complex number by its conjugate?

Back

The result is a real number: (a + bi)(a - bi) = a^2 + b^2.

Front

Calculate: (4 − 7i) − (−3 + 6i)

Back

7 − 13i

Front

What is i^7?

Back

-i

Front

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

Back

13 (since (2 + 3i)(2 - 3i) = 4 + 9 = 13).

Front

How do you divide complex numbers?

Back

Multiply the numerator and denominator by the conjugate of the denominator.

Front

What is the imaginary unit 'i'?

Back

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