Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Two complex numbers are given, where m, n, p, and q are real numbers.

m+ni
p+qi

For what relationship among m, n, p, and q, will be the product of these two complex numbers have only an imaginary part?

This is Algebra 2.

Sagot :

mhanifa

Answer:

Given complex numbers:

  • m+ni
  • p+qi

Their product is:

  • (m + ni)(p + qi) =
  • mp + npi + mqi + nqi² =
  • mp - nq + (np + mq)i

In order to have only an imaginary part we need:

  • mp - nq = 0

or

  • mp = nq

Answer:

First we have to find product

[tex]\\ \sf\longmapsto (m+ni)(p+qi)[/tex]

[tex]\\ \sf\longmapsto m(p+qi)+ni(p+qi)[/tex]

[tex]\\ \sf\longmapsto mp+mqi+npi+nqi^2[/tex]

[tex]\\ \sf\longmapsto mp+mqi+nqi-nq[/tex]

[tex]\\ \sf\longmapsto mp-nq+(mq+nq)i[/tex]

  • We have to keep imaginary parts i.e Im(z)

[tex]\\ \sf\longmapsto mp-nq=0[/tex]

[tex]\\ \sf\longmapsto mp=nq[/tex]

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.