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
Answer:
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
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Step-by-step explanation:
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