BICOL STATE COLLEGE OF APPLIED SCIENCES AND TECHNOLOGY
College of Engineering and Architecture
Advanced Engineering Mathematics
[@jjfm11] [PROBLEM SET] [ADVANCED ENGINEERING MATHEMATICS] [Page 1 of 3]
NAME:________________________________________ ________________________
SECTION:__________ ________ YEAR||COURSE:___________________ _______
PROBLEM SET#1
Part 1. OPERATIONS ON COMPLEX NUMBERS
Perform the indicated operation and express the result in polar form. Show complete
solution
EXPRESSION
ANSWER
(𝟓+𝐣𝟑)+(𝟔−𝐣𝟖)
𝟏𝟐.𝟎𝟖𝟑∠(−𝟐𝟒.𝟒𝟒°)
𝐣−𝟓+(𝟐−𝐣𝟑)−𝟏
𝟎.𝟕𝟖𝟒∠(−𝟕𝟖.𝟔𝟖°)
𝟑
(𝟐+𝐣𝟓)+𝟑
(𝟓+𝐣𝟐)
𝟏.𝟎𝟐𝟒∠(−𝟒𝟓°)
𝟓𝐜𝐣𝐬𝟑𝟎°+𝟐𝐞𝐣𝟎.𝟕𝟓𝟐−(𝟑+𝐣𝟓)
𝟑.𝟎𝟏𝟐∠(−𝟐𝟐.𝟏𝟏°)
𝟒+𝐣𝟑
𝟐−𝐣
𝟐.𝟐𝟑𝟔∠𝟔𝟑.𝟒𝟑°
(𝟑+𝐣𝟐)(𝟕∠𝟑𝟎°+𝐣𝟐)
𝟐𝟗.𝟓𝟏𝟑∠𝟕𝟓.𝟗𝟏°
(𝟔+𝐣𝟑)𝟐
𝟐−𝐣𝟐 +𝟖∠𝟑𝟎°
𝟐𝟎.𝟐𝟗𝟔∠𝟕𝟔.𝟔𝟕°
𝟏𝟐∠𝟑𝟎°+𝟖∠𝟐𝟓°−𝟔∠(−𝟐𝟎°)
𝟏𝟔.𝟓𝟕𝟖∠𝟒𝟑.𝟔𝟎°
𝐣𝟐𝟗+𝐣𝟐𝟏+𝐢
𝟑∠𝟗𝟎°
−𝟐−𝐣𝟑
𝟑+𝐣𝟒
𝟎.𝟕𝟐𝟏∠(−𝟏𝟕𝟔.𝟖𝟐°)
𝐣𝟑(𝟒−𝐣𝟓)(𝟔𝐜𝐣𝐬𝟐𝟓°)
𝟏𝟏𝟓.𝟐𝟓𝟔∠𝟔𝟑.𝟔𝟔°
𝟒𝟎𝐞𝐣𝟐𝛑
𝟑+𝟐𝟎∠(−𝟒𝟎°)+𝟐𝟔.𝟒𝟔+𝐣𝟎
𝟑𝟎.𝟖𝟎𝟔∠𝟒𝟓°
(𝟑+𝐣𝟒)𝟐[(𝟐𝐜𝐣𝐬𝟑𝟎°+𝟐∠𝟐𝟎°)+𝟔𝐞𝐣𝟎.𝟐𝟓𝟐]
(𝟑+𝐣𝟕)(𝟓𝐜𝐣𝐬𝟐𝟓°)+(𝟑∠𝟑𝟎°)𝟐
𝟓.𝟒𝟎𝟖∠𝟑𝟗.𝟎𝟑°
(𝟑+𝐣𝟓)𝟒
(𝟐+𝐣𝟔)𝟑
𝟒.𝟓𝟔𝟗∠𝟐𝟏.𝟒𝟓°
(𝟕+𝐣𝟖
𝟔−𝐣𝟑)(𝟒+𝐣𝟓
𝟖−𝐣𝟒)
𝟏.𝟏𝟑𝟒∠𝟏𝟓𝟑.𝟐𝟖°
𝟓+𝟑∠𝟐𝟎°+𝟑𝐣
𝟏−𝟑𝐣𝟐
𝟐.𝟏𝟗𝟗∠𝟐𝟕.𝟐𝟒°
If (𝐱+𝐣𝐲)𝟐=𝟑+𝐣𝟖, find x and y
𝐱=𝟐.𝟒𝟎𝟐
𝐲=𝟏.𝟔𝟔𝟓
Find the quadratic equation whose
roots are (𝟑−𝐣𝟓)𝐚𝐧𝐝 (𝟐 + 𝐣𝟒)
𝐱𝟐−𝟓.𝟎𝟗𝟗∠(−𝟏𝟏.𝟑𝟐°)𝐱+𝟐𝟔.𝟎𝟕𝟔∠𝟒.𝟑𝟗°=𝟎
(𝟒−𝟒√−𝟐𝟓)(𝟕+𝟓√−𝟑𝟔)
𝟔𝟐𝟖.𝟑𝟏𝟖∠(−𝟏.𝟖𝟐°)
(−𝟕+𝟓√−𝟔𝟒)𝟐
𝟖√−𝟏𝟔
𝟓𝟏.𝟓𝟑𝟏∠𝟏𝟎𝟗.𝟖𝟓°
