Answer: I found: −7−6i. Explanation: You need to get rid of the i at the denominator first. To do that you can multiply and divide by the complex ...
1 answer
Step-by-step explanation:
The quotient of [13/(5-i)] in the form of (a + bi) is (2.5 + 0.5i) and this can be determined by using the arithmetic operations.
Given :
Number --- [tex]\rm \dfrac{13}{5-i}[/tex]
The following steps can be used in order to determine the quotient of the given number in the form of (a+bi):
Step 1 - Write the given number.
[tex]\rm \dfrac{13}{5-i}[/tex]
Step 2 - Multiply and divide by (5 + i) in the above expression.
[tex]=\rm \dfrac{13}{5-i}\times \dfrac{5+i}{5+i}[/tex]
Step 3 - Multiply 13 by (5 + i) in the above expression.
[tex]=\rm \dfrac{65+13i}{(5-i)\times(5+i)}[/tex]
Step 4 - Multiply (5 - i) by (5 + i) in the above expression.
[tex]=\rm \dfrac{65+13i}{(25+5i-5i+1)}[/tex]
Step 5 - Further simplify the above expression.
[tex]=\rm \dfrac{65+13i}{(26)}[/tex]
= 2.5 + 0.5i
So, the quotient of [13/(5-i)] in the form of (a + bi) is (2.5 + 0.5i).
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https://brainly.com/question/15385899
