Monday, July 25, 2011

Practice problems with complex numbers a + bi


a] (4 + i) + (7 - i)
b] (4 + i) - (7 - i)
c] (7 - i) - (4 + i)
d] (4 + i) * (7 - i)
e] (4 + i) / (7 - i)
f] (7 - i) / (4 + i)

Answers in the comments.
   

1 comment:

Prof. Hubbard said...

a] (4 + i) + (7 - i)

Answer: 11

b] (4 + i) - (7 - i)

Answer: -3 + 2i

c] (7 - i) - (4 + i)

Answer: 3 - 2i

d] (4 + i) * (7 - i)

FOIL: 28 - 4i + 7i - i^2 =

28 - 4i + 7i + 1 =

Answer: 29 + 3i

e] (4 + i) / (7 - i)
Multiply by (7 + i)/(7 + i)

Numerator FOIL = 28 + 4i + 7i + i^2 =
28 + 4i + 7i - 1 =

27 + 11i

Denominator FOIL =
49 + 7i - 7i - i^2 =

49 + 7i - 7i + 1=
50

Answer: 27/50 + 11i/50


f] (7 - i) / (4 + i)

Multiply by (4 - i)/(4 - i)

Numerator FOIL = 28 - 7i - 4i + i^2 =
28 - 7i - 4i - 1 =
27 - 11i

Denominator FOIL =
16 - 4i + 4i - i^2 =

16 + 7i - 7i + 1=
17

Answer: 27/17 - 11i/17