Answer:
Complex numbers are the one having two parts:
Each of the part is simplified to (a+ib) format.
I hope it will help you.
Explanation:
All parts are solved below:
Part 1:
=(-8i) + (41)+(-3 - 7i)
opening brackets
=-8i+41-3-7i
Adding like terms, real to real and imaginary to imaginary
= 38-15i
Part 2:
= (7 + 5i) - (7 - i)
Negative sign before bracket will change the signs to opposite
=7+5i - 7+ i
Adding like terms, real to real and imaginary to imaginary
=0 + 6i
Part 3:
=(8 – 4i) - (5 – 4i)
Negative sign before bracket will change the signs to opposite
= 8-4i-5+4i
Adding like terms, real to real and imaginary to imaginary
=3+0i
Part 4:
=(-8 - 4i) - (8 + i)
Negative signs before bracket will change the signs to opposite
=-8-4i-8-i
Adding like terms, real to real and imaginary to imaginary
=-16-5i
Part 5:
=(-3 - i) + (7 + 2i)
=-3-i+7+2i
Adding like terms, real to real and imaginary to imaginary
=4+1i
Part 6:
=-2 +6-(-4 + 2i)
Negative sign before bracket will change the signs to opposite
=-2+6+4-2i
Adding like terms, real to real and imaginary to imaginary
=8-2i
Part 7:
=(3 - 8i)(-4 + 4i)
Multiplying both bracket we get:
=-12+12i+32i+32i^2
By putting i^2 = (-1)
=12 +44i + 32 (-1)
Adding like terms, real to real and imaginary to imaginary
= -20+44i
Part 8:
=(5 – 3i)(-7 - 2i)
Multiplying both bracket we get:
=-35-10i+21i+6i^2
=-31+11i + 6 (-1) (By putting i^2 = (-1))
Adding like terms, real to real and imaginary to imaginary
=-37+11i
Part 9:
=8 + 8i
Part 10:
=(7 - 5i)(-4 + 3i)
Multiplying both bracket we get:
=-28+21i+20i-15i^2 (By putting i^2 = (-1))
=-28+41i- 15(-1)
Adding like terms, real to real and imaginary to imaginary
=-13+41i
Part 11:
=7 + 4i
Part 12:
=(8 - 7i)(3 - 3i)
Multiplying both bracket we get:
=24-24i-21i+21i^2
=24-45i+21(-1) (By putting i^2 = (-1))
Adding like terms, real to real and imaginary to imaginary
=3-45i