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Question

Find $$a$$ and $$b$$, where $$a$$ and $$b$$ are real numbers so that 
$$a+ib={(2-i)}^{2}$$


A
a=3,b=4
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B
a=3,b=4
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C
a=3,b=4
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D
a=3,b=4
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Solution

The correct option is A $$a=3, b=-4$$
Solve the given expression as follows:
$$a+ib=(2-i)^2$$
$$a+ib=4+i^2-4i$$
$$a+ib=4-1-4i$$
$$a+ib=3-4i$$
The real term on the left is $$a$$, the real term on the right is $$3$$. These two are equal. 
The imaginary term on the left is $$b$$ and the imaginary term on the right is $$-4$$. These two are equal. 
Therefore, $$a=3$$, and $$b=-4$$.

Mathematics

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