21. What is the argument of the complex number (-1-i),
where i = √-1?
(b) – 5π÷4
(a) 5π÷4
(C) 3π÷4
(d) None of these
Answers
Answer:
Step-by-step explanation:
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
= (1/i4)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: