SOLUTION: Find the Modulus and argument of the following complex numbers, and write them in trigonometric form: A) {{{ 5-8i }}} B) {{{ -1- i }}} C) {{{ -5+12i }}} D) {{{ 1+ sqrt(3i)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the Modulus and argument of the following complex numbers, and write them in trigonometric form: A) {{{ 5-8i }}} B) {{{ -1- i }}} C) {{{ -5+12i }}} D) {{{ 1+ sqrt(3i)       Log On


   

Question 1077346: Find the Modulus and argument of the following complex numbers, and write them in trigonometric form:
A) +5-8i+
B) +-1-+i+
C) +-5%2B12i+
D) 1+ sqrt(3i)
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the Modulus and argument of the following complex numbers, and write them in trigonometric form: 

A) 5-8i         The modulus is sqrt%285%5E2+%2B+%28-8%29%5E2%29 = sqrt%2889%29.
                 The argument is arctan%28%28-8%29%2F5%29.


B) -1-+i         The modulus is sqrt%28%28-1%29%5E2+%2B+%28-1%29%5E2%29 = sqrt%282%29.
                 The argument is pi+%2B+arctan%281%29 = 5pi%2F4.


C) -5%2B12i+       The modulus is sqrt%28%28-5%29%5E2+%2B+12%5E2%29 = sqrt%28169%29 = 13.
                 The argument is pi+-+arctan%2812%2F5%29.


D) 1%2B+sqrt%283%29i         The modulus is sqrt%281%5E2+%2B+sqrt%283%29%5E2%29 = sqrt%281%2B3%29 = 2.
                 The argument is arctan%28sqrt%283%29%29 = pi%2F3.


On complex numbers, modulus and arguments, see the lessons
    - Complex numbers and arithmetic operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power
    - How to take a root of a complex number
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Complex numbers".


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Notice that you incorrectly wrote your complex number in D).
I fixed your error in my response.