Friday
November 28, 2014

Homework Help: Maths

Posted by Tom on Sunday, January 21, 2007 at 5:08am.

use the formula
cos(x+iy)=cosxcosiy-sinxsiniy
to find two imaginary numbers whose cosine is 3

cos(x+iy)=cosxcosiy-sinxsiniy =

cos(x)cosh(y) - i sin(x)sinh(y) = 3

Equating imaginary parts gives:

sin(x)sinh(y) = 0

You know that y cannot be zero, otherwise the complex number woyuld be real, but for real arguments the cosine is always between -1 and 1. If y is not zero, sinh(y) is not zero, and therefore sin(x) must be zero. This means that x is an integer times pi.

x = n pi

Equating the real parts gives:


cos(x)cosh(y) = 3

Insert x = n pi, using

cos(n pi) = (-1)^n

gives:

cosh(y) = 3*(-1)^n

cosh for real arguments is always positive, so n must be even. And we see that:

y = arccosh(3)

So, the complex numbers are of the form:

2n pi + arccosh(3)i

Thanks

thanks

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

maths 2 - The original question I had was write arcsin4 in the form a+ib. I ...
Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
tigonometry - expres the following as sums and differences of sines or cosines ...
trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
algebra - Can someone please help me do this problem? That would be great! ...
Math - Calculus - The identity below is significant because it relates 3 ...
Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
Calculus II - What is sin(i) -- (sin of the imaginary number, i) What is cos(i...

Search
Members