1
(x - iy) - (n - iv)
Chapter 29 · Imaginaries
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
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0of 10 done
From Imaginary and Complex Numbers, exercise 18
Simplify:
From Equations with Imaginary Roots, exercise 14
Solve and check the equations which follow (give every root):
2
How many square roots has any real number (not zero)? cube roots? fourth roots? sixth roots? (Use Exercises 7–13.)
From Multiplication of Imaginaries, exercise 1
Perform the indicated multiplications and simplify results:
3
\left(\sqrt{-1}\right)^5
From Imaginary and Complex Numbers, exercise 9
Simplify:
4
3 + 2\sqrt{-1} + 5 - 6\sqrt{-1}
From Division of Imaginaries, exercise 4
Perform the indicated division:
5
\sqrt[4]{-1} \div \sqrt[4]{-4}
From Division of Imaginaries, exercise 15
Perform the indicated division:
6
\dfrac{-1 + \sqrt{-3}}{-1 - \sqrt{-3}}
From Multiplication of Imaginaries, exercise 11
Perform the indicated multiplications and simplify results:
7
4\sqrt{-5}\left(-3\sqrt{-6}\right)
From Multiplication of Imaginaries, exercise 10
Perform the indicated multiplications and simplify results:
8
\sqrt{-m} \cdot \sqrt{-n}
From Multiplication of Imaginaries, exercise 12
Perform the indicated multiplications and simplify results:
9
\sqrt{a + b} \cdot \sqrt{-a - b}
From Division of Imaginaries, exercise 17
Perform the indicated division:
10
\dfrac{a}{a + bi}