Question

Find the modulus and the principal arguement of each of the given complex numbers
a. 3-4i b. -2+i c. 1/1+i(2)½ d. 7-i/-3-3i

Answer 1

a. $|3-4i|=\sqrt{9+16}=5,arg(3-4i)=\arctan (-4/3)\approx-53^0$

b.$|-2+i|=\sqrt{4+1}=\sqrt5,arg(-2+i)=\arctan(-1/2)+180^0\approx153.4^0$

c.$|\frac{1}{1+\sqrt2i}|=|\frac{1-i\sqrt2}{1+2}|=|1/3-i\sqrt2/3|=\sqrt{1/9+2/9}=\sqrt3/3$

$arg\frac{1}{1+i\sqrt2}=\arctan(-\sqrt2)\approx54.7^0$

d.$|\frac{7-i}{-3-3i}|=|-\frac{(7-i)(1-i)}{3\sdot2}|=|-1+i4/3|=\sqrt{1+16/9}=5/3$

$arg(-1+i4/3)=\arctan(-4/3)+180^0\approx127^0$