Question

4) Express the following in the form of a+ib,
a, beR i =V-1. State the values of a and b.
i) (1+2i)(-2+i) ii) (1+i)(1-1)-1
i(4+3i)
(2+i)
iv) (3-1) (1+2i)
iii)(1i)
3+2i 3-2i
vì) 2-5i 2+5i
vi) (1+) vii) 21 V-3
ix) (-V5 +21-4)+(1-V-9)+(2+3i)(2 – 3i)
4i8 – 31° +3
x) (2+3i)(2–3i) xi) 3711 _ 1;10 _5​

Answer 1

Answer:

1)

(1+2i)(-2+i)

= -2 + i - 4i + i²

= -2 - 3i - 1

= -3 - 3i

Here

a = -3 and b = -3

2)

(1+i)(1-1)-1i(4 + 3i)(2 +i)

= (1 + i)(0) - 1i(4 + 3i)(2 +i)

= 0 - 1i(4 + 3i)(2 + i)

= -1i(4 + 3i)(2 + i) = (3 - 4i)(2+ i)

= 6 + 3i - 8i - 4i²

= 6 - 5i + 4

= 10  - 5i

Here

a = 10     and    b = -5

3)

(1i) (3+2i)(3-2i)

= (i)(3² - i²)

= i(9 + 1)

= 10i = 0 + 10i

Here

a = 0   and b = 10

4)

 (3-1)(1+2i)

= 3 + 6i - 1 - 2i

= 2 + 4i

Here

a = 2   and   b = 4

5)

21 V-3

= 21√3√-1

= (21√3)i            ∵ √(-1) = i

= 0 + (21√3)i  

Here

a = 0   and   b = (21√3)

Do in the same way others

Answer 2

Answer:

1)

(1+2i)(-2+i)

= -2 + i - 4i + i²

= -2 - 3i - 1

= -3 - 3i

Here

a = -3 and b = -3

2)

(1+i)(1-1)-1i(4 + 3i)(2 +i)

= (1 + i)(0) - 1i(4 + 3i)(2 +i)

= 0 - 1i(4 + 3i)(2 + i)

= -1i(4 + 3i)(2 + i) = (3 - 4i)(2+ i)

= 6 + 3i - 8i - 4i²

= 6 - 5i + 4

= 10  - 5i

Here

a = 10     and    b = -5

3)

(1i) (3+2i)(3-2i)

= (i)(3² - i²)

= i(9 + 1)

= 10i = 0 + 10i

Here

a = 0   and b = 10

4)

(3-1)(1+2i)

= 3 + 6i - 1 - 2i

= 2 + 4i

Here

a = 2   and   b = 4

5)

21 V-3

= 21√3√-1

= (21√3)i            ∵ √(-1) = i

= 0 + (21√3)i  

Here

a = 0   and   b = (21√3)

Step-by-step explanation:1)