Question

Algebra 2

Answer 1

Answer:

Complex numbers are the one having two parts:

• Real part
• Imaginary part

Each of the part is simplified to (a+ib) format.

I hope it will help you.

Step-by-step 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