Question

I just need answers to the odd numbered questions.

I would appreciate the help

35 points

Answer 1

Explanation:

Combine real terms and combine complex terms

1) 3 + 2i + 2 - 5i = 3 +2 + 2i - 5i

= 5 + (2-5)i

= 5 + (-3)i

= 5 - 3i

3) 2 - (1 - 2i) + (4 -5i ) - (1 - 3i) = 2 -1 + 2i + 4 - 5i - 1 + 3i

{- is distributed to (1 - 2i) & - is distributed to (1- 3i)}

= 2 - 1 + 4 + 1 + 2i - 5i + 3i

= 6 +0i = 6

5) 4 - 3i + 4 + 3i = 4 +4 -3i + 3i

= 8

7) (3 - 2i)² + (3 +2i) = 3² - 2*3*2i + (2i)² + 3 + 2i {(a - b)² = a² - 2ab +b²}

= 9 -12i + 4i² + 3 + 2i

= 9 - 12i + 4*(-1) + 3 + 2i {i² = -1}

= 9 +3 - 4 - 12i +2i

= 8 - 10i

`9) (a +b)^(4) - (a - b)^(4) = 8ab(a^(2) +b^(2))\\\\\\Here, \ a = 1 \ and \ b = i\\\\\\(1+√(-1))^(4)-(1-√(-1))^(4)=(1+\sqrt{i^(2)})^(4)-(1-\sqrt{i^(2)})^(4)\\\\=(1+i)^(4)-(1-i)^(4)\\\\=8*1*i(1^(2)+i^(2))\\\\=8i*(1 -1)\\\\=8i*0\\\\=0`