Engineering Mathematics

Stroud, K. A. Booth, Dexter J.

Chapter 14

Complex numbers 1 - all with Video Answers

Educators

Section 1

Test exercise F.1

Problem 1

You will find the questions quite straightforward and easy.
Simplify: (a) $j^{3}$
(b) $j^{5}$
(c) $j^{12}$
(d) $j^{14}$.

M Hassan Anwar

M Hassan Anwar

Numerade Educator

Problem 2

CMS/BOTTLER LINK: https://bottler.numerade.com/book/detail/1877/1/10Express in the form $a+j b$ :
(a) $(4-j 7)(2+j 3)$
(b) $(-1+j)^{2}$
(c) $(5+j 2)(4-j 5)(2+j 3)$
(d) $\frac{4+j 3}{2-j}$

Mir Afzal

Numerade Educator

Problem 2

You will find the questions quite straightforward and easy.
Express in the form $a+j b$ :
(a) $(4-j 7)(2+j 3)$
(b) $(-1+j)^{2}$
(c) $(5+j 2)(4-j 5)(2+j 3)$
(d) $\frac{4+j 3}{2-j}$

M Hassan Anwar

Numerade Educator

Problem 3

You will find the questions quite straightforward and easy.
Find the values of $x$ and $y$ that satisfy the equation: $(x+y)+j(x-y)=14 \cdot 8+j 6 \cdot 2$

M Hassan Anwar

Numerade Educator

Problem 4

You will find the questions quite straightforward and easy.
Express in polar form:
(a) $3+j 5$
(b) $-6+j 3$
(c) $-4-j 5$

M Hassan Anwar

Numerade Educator

Problem 5

You will find the questions quite straightforward and easy.
Express in the form $a+j b$ :
(a) $5\left(\cos 225^{\circ}+j \sin 225^{\circ}\right)$
(b) $4 \underline{330^{\circ}}$

M Hassan Anwar

Numerade Educator

Problem 6

You will find the questions quite straightforward and easy.
Express in exponential form:
(a) $z_{1}=10\left\lfloor 37^{\circ} 15^{\prime} \quad\right.$ and
(b) $\mathrm{z}_{2}=10 \underline{322}{45^{\prime}}$
Hence find $\ln z_{1}$ and $\ln z_{2}$

M Hassan Anwar

Numerade Educator

Problem 7

You will find the questions quite straightforward and easy.
Express $z=e^{1+j \pi / 2}$ in the form $a+j b$.

M Hassan Anwar

Numerade Educator