Записать число в трех формах Z=4/1+i*корень из 3

Question

0

1460

1

Guest May 6, 2015

+33615

+10

Best Answer

I think this is asking for 3 ways of writing z = 4/(1+i√3)

1. Multiply numerator and denominator by 1 - i√3: 4(1 - i√3)/(1+3), so z = 1 - i√3

2. |z| = √(1+3) = 2, tan^-1(-√3/1) = -pi/3: z = 2e^-i*pi/3

3. e^iθ = cos(θ) + i*sin(θ), so z = 2cos(pi/3) - 2i*sin(pi/3)

.

Alan May 6, 2015

Alan · Answer 1 · 2015-05-06T03:42:04

I think this is asking for 3 ways of writing z = 4/(1+i√3)

1. Multiply numerator and denominator by 1 - i√3: 4(1 - i√3)/(1+3), so z = 1 - i√3

2. |z| = √(1+3) = 2, tan^-1(-√3/1) = -pi/3: z = 2e^-i*pi/3

3. e^iθ = cos(θ) + i*sin(θ), so z = 2cos(pi/3) - 2i*sin(pi/3)

.