Math, asked by ethutty2004, 4 months ago

1. 3(7+i7) + I(7+i7)
2.( 1-i) - (-1+i6)
3. (1/5 + i2/5)
4. [(1/3 + i7/3)] - (-4/3+i)
5. (1-i)⁴
6. (1/3+3i)³
7. (-2-1/3i)ㅤ

Find the multiplicative inverse of each of the complex numbers given in exercises 1 to 7 .

Answers

Answered by Itzsweetcookie
2

Answer:

☺HOPE \: ITS \: HELPFUL❤

Question 1:

Express the given complex number in the form a + ib: (5i)(-3i/5)

Answer:

(5i)(-3i/5) = (-5 * 3/5) * i * i

                   = -3 * i2

                   = -3 * (-1)                  [Since i2 = -1]

                   = 3

Question 2:

Express the given complex number in the form a + ib: i9 + i19

Answer:

i9 + i19 = i4*2 + 1 + i4*4 + 3

            = (i4)2 * i + (i4)4 * i3

            = (1)2 * i + (1)4 * i * i2                 [Since i4 = 1]

            = i + i * (-1)                                  [Since i2 = -1]

            = i – i

            = 0

Question 3:

Express the given complex number in the form a + ib: i-39

Answer:

i-39 = i-4 * 9 - 3

     = (i-4)9 * i-3

     = 19 * i-3                     [Since i4 = 1]

    = i-3

    = 1/ i3

    = i4/ i3                        [Since i4 = 1]

    = i

Question 4:

Express the given complex number in the form a + ib:  3(7 + i7) + i(7 + i7)

Answer:

Given, 3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i2

                                              = 21 + 21i + 7i - 7            [Since i2 = -1]

                                              = 14 + 28i

Question 5:

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

Answer:

Given, (1 – i) – (–1 + i6) = 1 – i + 1 - 6i

                                          = 2 - 7i   

Question 6:

Express the given complex number in the form a + ib: (1/5 + 2i/5) – (4 + 5i/2)

Answer:

Given, (1/5 + 2i/5) – (4 + 5i/2) = 1/5 + 2i/5 – 4 - 5i/2

                                                      = (1/5 - 4) + (2i/5 - 5i/2)

                                                      = -19/5 + (4i - 25i)/10    

                                                      = -19/5 - 21i/10     

 

Question 7:

Express the given complex number in the form a + ib: [(1/3 + 7i/3) + (4 + i/3)] – (-4/3 + i)

Answer:

Given, [(1/3 + 7i/3) + (4 + i/3)] – (-4/3 + i) = 1/3 + 7i/3 + 4 + i/3 + 4/3 – i

                                                                          = (1/3 + 4 + 4/3) + i(7/3 + 1/3 - 1)

                                                                          = 17/3 + 5i/3


ethutty2004: thank you so much
Answered by patidarpragya111
0

wes23" vvbhgffccccggg

Step-by-step explanation:

fgghjkkkhvv vgj


ethutty2004: mm ok
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