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Chapter 11: Problem 1

Write down an expression for (a) \(\sqrt{4}\), (b) \(\sqrt{-4}\), (c) \(\sqrt{81}\), (d) \(\sqrt{-81}\)

Short Answer

Expert verified
Question: Find the square roots of the following numbers: (a) 4, (b) -4, (c) 81, (d) -81. Solution: (a) The square root of 4 is 2, since 2 * 2 = 4. (b) The square root of -4 is 2i, because (2i) * (2i) = 4 * (-1) = -4. (c) The square root of 81 is 9, since 9 * 9 = 81. (d) The square root of -81 is 9i, because (9i) * (9i) = 81 * (-1) = -81.

Step by step solution

01

(a) Square root of 4

To find the square root of 4, we want to find a number that, when multiplied by itself, results in 4. In this case, the square root of 4 is 2, because 2 * 2 = 4. So, \(\sqrt{4} = 2\).
02

(b) Square root of -4

To find the square root of -4, we want to find a number that, when multiplied by itself, results in -4. We can use the imaginary unit i, where i represents the square root of -1. In this case, the square root of -4 is 2i, because (2i) * (2i) = 4 * (-1) = -4. So, \(\sqrt{-4} = 2i\).
03

(c) Square root of 81

To find the square root of 81, we want to find a number that, when multiplied by itself, results in 81. In this case, the square root of 81 is 9, because 9 * 9 = 81. So, \(\sqrt{81} = 9\).
04

(d) Square root of -81

To find the square root of -81, we want to find a number that, when multiplied by itself, results in -81. Again, we can use the imaginary unit i, where i represents the square root of -1. In this case, the square root of -81 is 9i, because (9i) * (9i) = 81 * (-1) = -81. So, \(\sqrt{-81} = 9i\).

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Most popular questions from this chapter

Solve each of the following equations leaving (a) \(z^{3}=-1\) (b) \(z^{3}=1\) (c) \(z^{3}-6 \mathrm{j}=0\) your answers in polar form: (a) \(z^{2}=1+\mathrm{j}\) (b) \(z^{2}=1-\mathrm{j}\) (c) \(z^{3}=-2+3 \mathrm{j}\)

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