The square root of (1- 2i) is(1) V5 (cos ( + 2n) + i sin ( + 2n)) for n = 0, 1(2) 5 (cos ( + 2n) + i sin ( + 20)) for n =0, 137T72nn(3) V5 (cos ( + 2) + i sin ( + 2)) for n = 0, 1O A. None of the given answers is trueB. Option (1) is true.OC. Option (2) is true.D. Option (3) is true.Reset Selection

Answered: The square root of (1 2i) is (1) V5…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The square root of (1- 2i) is
(1) V5 (cos ( + 2n) + i sin ( + 2n)) for n = 0, 1
(2) 5 (cos ( + 2n) + i sin ( + 20)) for n =
0, 1
3
7T7
2nn
(3) V5 (cos ( + 2) + i sin ( + 2)) for n = 0, 1
O A. None of the given answers is true
B. Option (1) is true.
OC. Option (2) is true.
D. Option (3) is true.
Reset Selection

Expert Solution

Step 1

The general form of a complex number is given by $z = a + i b$ , where a,b are two real numbers and $i = \sqrt{- 1}$ . The magnitude of a complex number $z = a + i b$ is defined as $| z | = \sqrt{a^{2} + b^{2}}$ .

Any complex number in the form $z = a + i b$ can be represented in the form $z = r e^{i θ}$ , where $r = \sqrt{a^{2} + b^{2}}$ and $θ = \tan^{- 1} \frac{y}{x}$ . Since $e^{i θ} = \cos θ + i \sin θ$ , the alternate form of the complex number $z = a + i b$ is $z = r (\cos θ + i \sin θ)$ .