Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Algebra for IIT JAM Mathematics

Created by: Veda Institute

Mathematics : Problems for Practice - Complex Numbers Mathematics Notes | EduRev

The document Problems for Practice - Complex Numbers Mathematics Notes | EduRev is a part of the Mathematics Course Algebra for IIT JAM Mathematics.
All you need of Mathematics at this link: Mathematics

Complex Numbers - Practice Problems
Perform the indicated operation and write your answer in standard form.
Q.1. (4−5i)(12+11i)(4−5i)(12+11i)
Ans. We know how to multiply two polynomials and so we also know how to multiply two complex numbers. All we need to do is “foil” the two complex numbers to get,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
All we need to do to finish the problem is to recall that i2=−1. Upon using this fact we can finish the problem.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.2. (−3−i)−(6−7i)
Ans. We know how to subtract two polynomials and so we also know how to subtract two complex numbers.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.3. (1+4i)−(−16+9i)
Ans. 
We know how to subtract two polynomials and so we also know how to subtract two complex numbers.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.4. 8i(10+2i) 
Ans. We know how to multiply two polynomials and so we also know how to multiply two complex numbers. All we need to do is distribute the 8i to get,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
All we need to do to finish the problem is to recall that i2=−1. Upon using this fact we can finish the problem.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.5. (−3−9i)(1+10i)
Ans. We know how to multiply two polynomials and so we also know how to multiply two complex numbers. All we need to do is “foil” the two complex numbers to get,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
All we need to do to finish the problem is to recall that i2=−1. Upon using this fact we can finish the problem.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.6. (2+7i)(8+3i)
Ans. We know how to multiply two polynomials and so we also know how to multiply two complex numbers. All we need to do is “foil” the two complex numbers to get,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
All we need to do to finish the problem is to recall that i2=−1. Upon using this fact we can finish the problem.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.7. Problems for Practice - Complex Numbers Mathematics Notes | EduRev
Ans. Because standard form does not allow for i’s to be in the denominator we’ll need to multiply the numerator and denominator by the conjugate of the denominator, which is 2−10i.
Multiplying by the conjugate gives,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
Now all we need to do is do the multiplication in the numerator and denominator and put the result in standard form.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.8. Problems for Practice - Complex Numbers Mathematics Notes | EduRev
Ans. Because standard form does not allow for ii’s to be in the denominator we’ll need to multiply the numerator and denominator by the conjugate of the denominator, which is 3i.
Multiplying by the conjugate gives,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
Now all we need to do is do the multiplication in the numerator and denominator and put the result in standard form.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Q.9.Problems for Practice - Complex Numbers Mathematics Notes | EduRev
Ans. Because standard form does not allow for i’s to be in the denominator we’ll need to multiply the numerator and denominator by the conjugate of the denominator, which is 8+i.
Multiplying by the conjugate gives,
Problems for Practice - Complex Numbers Mathematics Notes | EduRev
Now all we need to do is do the multiplication in the numerator and denominator and put the result in standard form.
Problems for Practice - Complex Numbers Mathematics Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Dynamic Test

Content Category

Related Searches

study material

,

Extra Questions

,

Summary

,

Problems for Practice - Complex Numbers Mathematics Notes | EduRev

,

Previous Year Questions with Solutions

,

Viva Questions

,

Exam

,

Problems for Practice - Complex Numbers Mathematics Notes | EduRev

,

Sample Paper

,

shortcuts and tricks

,

Objective type Questions

,

Problems for Practice - Complex Numbers Mathematics Notes | EduRev

,

MCQs

,

Semester Notes

,

Free

,

video lectures

,

Important questions

,

past year papers

,

ppt

,

practice quizzes

,

mock tests for examination

,

pdf

;