Answered: (1+i)^2(4+i)/(3-i) find magnitude real…

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

(1+i)^2(4+i)/(3-i) find magnitude real and imaginary part

Expert Solution

Step 1

The given complex number is $\frac{{(1 + i)}^{2} (4 + i)}{3 - i}$ .

Rationalize the denominator as simplify as follows.

$\begin{array}{rcl} \frac{{(1 + i)}^{2} (4 + i)}{3 - i} & = & \frac{{(1 + i)}^{2} (4 + i)}{3 - i} \times \frac{3 + i}{3 + i} \\ = & \frac{{(1 + i)}^{2} (4 + i) (3 + i)}{(3 - i) (3 + i)} \\ = & \frac{[1 + i^{2} + 2 i] [12 + 7 i + i^{2}]}{3^{2} - i^{2}} \\ = & \frac{[1 - 1 + 2 i] [12 + 7 i - 1]}{9 - (- 1)} (i^{2} = - 1) \\ = & \frac{[2 i] [11 + 7 i]}{10} \end{array}$

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