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# Basic Complex Numbers Question (Edex. P4) watch

1. The question is:

Express: (1 + 2i)² + (3 - i)³ in the form a + bi.

I get 15 - 24i, but the book gets 15 - 22i. I am fairly sure that I'll be wrong.

Thank you.

Ref: P4, Ex 3a, 3(d).
2. The book is right.
3. (Original post by samd)
The question is:

Express: (1 + 2i)² + (3 - i)³ in the form a + bi.

I get 15 - 24i, but the book gets 15 - 22i. I am fairly sure that I'll be wrong.

Thank you.

Ref: P4, Ex 3a, 3(d).
The book is right.
4. (Original post by samd)
The question is:

Express: (1 + 2i)² + (3 - i)³ in the form a + bi.

I get 15 - 24i, but the book gets 15 - 22i. I am fairly sure that I'll be wrong.

Thank you.

Ref: P4, Ex 3a, 3(d).
(1 + 2i)(1 + 2i) = 1 + 4i + 4i2
= 4i - 3

(3 - i)(3 - i)(3 - i) = (9 - 6i + i2)(3 - i)
= 27 - 18i + 3i2 - 9i + 6i2 -i3
= 18 - 26i

Adding these gives 15 - 22i
5. (Original post by samd)
The question is:

Express: (1 + 2i)² + (3 - i)³ in the form a + bi.

I get 15 - 24i, but the book gets 15 - 22i. I am fairly sure that I'll be wrong.

Thank you.

Ref: P4, Ex 3a, 3(d).
With binomial theorem you get

1 + 4i - 4 + 27 - 27i - 9 + i
6. Thank you everyone.

I tried to do it by the Bionomial but wrote (-i)3 as -i, when really it is -i x -i x -i => -1 x -i = i.

Thanks again.

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