Roots of complex numbers
Answers are for parents and teachers.
1
Find all values of √(−49).
7i and −7i
2
Find the square roots of z = 4(cos 100° + i sin 100°).
2(cos 50° + i sin 50°) and 2(cos 230° + i sin 230°)
3
Write the three cube roots of 1 in algebraic form.
1; −1/2 + (√3/2)i; −1/2 − (√3/2)i
4
Find the fourth roots of 1.
1, i, −1, −i
5
Why do the roots of 1 form the vertices of a regular polygon on the unit circle?
All roots have modulus 1 and their arguments increase in steps of 360°/n, dividing the circle into equal parts.