Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

The complex numbers $z_1$ and $z_2$ are such that $|z_1| = 5,$ $|z_2| = 13,$ and
\[13z_1 - 5z_2 = 27 - 99i.\]find $z_1 z_2.$

Sagot :

xero099

By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

How to determine two complex numbers based on their norms and a given operation

In this question we must derive two complex numbers such that the following conditions are fulfilled:

a² + b² = 5²     (1)

c² + d² = 13²     (2)

13 · (a + i b) - 5 · (c + i d) = 27 - i 99     (3)

If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):

13 · (4 - i 3) - 5 · (5 + i 12)

52 - i 39 - 25 - i 60

27 - i 99

By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

To learn more on complex numbers: https://brainly.com/question/10251853

#SPJ1

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.