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Practice: Powers and Roots of Complex Numbers

Related Topics

Wize University Linear Algebra Textbook > Complex Numbers

Powers and Roots

5 Activities

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(a) If u=−32−12iu=-\frac{\sqrt{3}}{2}-\frac{1}{2}i, find u60u^{60}

(b) Find all three (complex) cube roots of 8

More Powers and Roots Questions:
Suppose f(x)f(x) is a polynomial of degree nnwith coefficients in C\mathbb{C}. Consider the following statements:
(i) If z=a+biz = a + bi is a root of f(x)f(x), then so is z=a−biz = a - bi.
(ii) If n=2n = 2 and f(x)f(x) has a nonzero linear term, then f(x)f(x) can only have roots if its coefficients are real.
If z=1−3iz = 1- \sqrt{3}i, then z6z^6 equals
If z=4−4iz = 4-4i, find z8z^8.
If w=2−2iw=\sqrt{2}-\sqrt{2}i, find w8w^8.
Which of the following is a 5th root of −i-i?
If z=32+12iz=\frac{\sqrt{3}}{2}+\frac{1}{2}i, then find z9z^9
Which of the following is a fourth root of the complex number z=−1+iz = -1 + i ?
Complex roots
Find all of the solutions (real and complex) to the equation z6−729=0z^6-729=0