complex numbers in the standard form of a complex number

Question

u=2-3i

v=-3+i

Write the following complex numbers in the standard form of a complex number.

u+v=

u-v=

uv=

u/v=

v/u=

v²=

v³=

v⁴=

 

Answer 1

u = (2 - 3i)
v = (-3 + i)

u+v = (2 - 3i) + (-3 + i) = (2-3) + (-3+1)i = -1 - 2i
u-v = (2 - 3i) - (-3 + i) = 2 - 3i + 3 - i = 5 - 4i
uv = (2 - 3i)(-3 + i) = -6 + 2i + 9i - 3i^2 = -6 + 11i + 3 = -3 +11i
u/v = (2 - 3i)/(-3 + i) = ((3 + i)(2 - 3i))/((3 + i)(-3 + i)) = (9 - 7i)/(-10)
v/u = (-3 + i)/(2 - 3i) = ((2 + 3i)(-3 + i))/((2 + 3i)(2 - 3i)) = (-9 - 7i)/13
v^2 = (-3 + i)^2 = 9 - 6i - 1 = 8 - 6i
v^3 = (-3 + i)^3 = (8 - 6i)(-3 + i) = -24 + 8i+ 18i + 6 = -18 + 26i
v^4 = (-3 + i)^4 = (-18 + 26i)(-3 + i) = 54 - 18i - 78i - 26 = 28 - 96i