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Anton [14]
3 years ago
10

Algebra 2

Mathematics
1 answer:
denis23 [38]3 years ago
3 0

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

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Answer:

The clock face is divided into sixty equal parts, each minute. The minute hand is located on the 20 minute mark at 6:20, the hour hand located between the 30 minute mark and the 35 minute mark. When the minute hand goes all sixty minutes, the hour hand only moves five, so to figure out the location of the hour hand, we look at how much the hour has progressed, in this case 20 minutes, or one third of the hour. So the minute hand has moved one third of the way through the hour, so has the hour hand moved one third of the way through the five minutes, or, five thirds of a minute, which is one and two thirds minute, one minute forty seconds. That puts the hour hand at thirty minutes plus one minute and forty seconds—at 31min 40sec—which is 11min 40sec farther than the minute hand.

Step-by-step explanation:

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