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Evaluate the expression 1+√−1 / 4+√−9 and write the result in the form a+bi

Question

Evaluate the expression 1+√−1 / 4+√−9 and write the result in the form a+bi

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Step 1

To evaluate

 

1+
4+9
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1+ 4+9

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Step 2

On simplifying the above ...

1+1
1+
4+3-1
4+-9
1i
[Using i
4 3
1 i
4-3i
[On rationalizing]
4 3i 4 3i
(14-3
(4 3)4-31
4-3i+4-3i2
Using (a+b)a-b) = a -b,/=-1]
(4)(3i)
4 3
16 9
7 i
25
7
1
=-
25 25
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1+1 1+ 4+3-1 4+-9 1i [Using i 4 3 1 i 4-3i [On rationalizing] 4 3i 4 3i (14-3 (4 3)4-31 4-3i+4-3i2 Using (a+b)a-b) = a -b,/=-1] (4)(3i) 4 3 16 9 7 i 25 7 1 =- 25 25

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Tagged in

Math

Algebra

Complex Numbers

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