Question

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

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

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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