Select the correct answer.If 2 i 2 + i − 3 i 3 + i...

doodverft05

doodverft05

Answered

2022-06-25

Select the correct answer.
If 2 i 2 + i 3 i 3 + i = a + b i, then a=_ and b=_.
1/10
-10
1/50
-1/10

Answer & Explanation

EreneDreaceaw

EreneDreaceaw

Expert

2022-06-26Added 20 answers

Step 1
Given that
2 i 2 + i 3 i 3 + i = a + b i
Step 2
2 i 2 + i × 2 i 2 i 3 i 3 + i × 3 i 3 i
Since ( a + b ) ( a b ) = a 2 b 2
2 i ( 2 i ) 2 2 i 2 3 i ( 3 i ) 3 2 i 2
4 i 2 i 4 + i 9 i 3 i 2 9 + i
4 i + 2 5 9 i + 3 10       i 2 = 2
8 i + 4 9 i 3 10
i + i 10 1 10 i 10
Compare with a+ib
a = 1 10 , b = 1 10

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