(Review of Complex Numbers) The three most important facts to know about complex numbers are that ⚫ every complex number can be written in the form a + bi, where a and b are real numbers ⚫eit = cos(t) +isin(t) (this is known as Euler's formula) When manipulating complex numbers, you are free to always treat i as you would with normal algebra (in terms of factoring, rearranging, etc.). If you ever have an i², you can replace it with -1. To divide complex numbers, you can multiply a fraction's numerator and denominator by the complex conjugate of the denominator, and then simplify: a+bi a+bi c-di c+ di cdi cdi You should be able to rearrange it to something of the form A + Bi, where A and B are real numbers. Write each of the following numbers in the form a + bi, where a and b are real numbers. (e) 2 (f) √i
(Review of Complex Numbers) The three most important facts to know about complex numbers are that ⚫ every complex number can be written in the form a + bi, where a and b are real numbers ⚫eit = cos(t) +isin(t) (this is known as Euler's formula) When manipulating complex numbers, you are free to always treat i as you would with normal algebra (in terms of factoring, rearranging, etc.). If you ever have an i², you can replace it with -1. To divide complex numbers, you can multiply a fraction's numerator and denominator by the complex conjugate of the denominator, and then simplify: a+bi a+bi c-di c+ di cdi cdi You should be able to rearrange it to something of the form A + Bi, where A and B are real numbers. Write each of the following numbers in the form a + bi, where a and b are real numbers. (e) 2 (f) √i
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(Review of Complex Numbers) The three most important facts to know about complex numbers are that
⚫ every complex number can be written in the form a + bi, where a and b are real numbers
⚫eit = cos(t) +isin(t) (this is known as Euler's formula)
When manipulating complex numbers, you are free to always treat i as you would with normal algebra (in terms of
factoring, rearranging, etc.). If you ever have an i², you can replace it with -1. To divide complex numbers, you can
multiply a fraction's numerator and denominator by the complex conjugate of the denominator, and then simplify:
a+bi
a+bi c-di
c+ di cdi cdi
You should be able to rearrange it to something of the form A + Bi, where A and B are real numbers. Write each of
the following numbers in the form a + bi, where a and b are real numbers.
(e) 2
(f) √i
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