Find the square root of the complex number, calculate the magnitude of the numberand its square roots, and plot all the points on the given complex plane.z=3+4ier:W.

Answered: Find the square root of the complex…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Find the square root of the complex number, calculate the magnitude of the number
and its square roots, and plot all the points on the given complex plane.
z=3+4i
er:
W.

Expert Solution

Step 1

Consider the complex number $3 + 4 i$ .

Find the square root of complex number.

let the square root of $3 + 4 i$ be $x + i y$ that is, $\sqrt{3 + 4 i} = x + i y$ .

Squaring both sides.

$\begin{array}{rcl} 3 + 4 i & = & {(x + i y)}^{2} \\ = & x^{2} + {(i y)}^{2} + i 2 x y (Identity {(A + B)}^{2} = A^{2} + B^{2} + 2 AB) \\ = & x^{2} - y^{2} + i 2 x y (i^{2} = - 1) \end{array}$

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