Still have math questions?

Ask our expert tutors
Arithmetic
Question

3. Suppose \( m = 2 + 6 i \) , and \( | m - n | - ...

3. Suppose \( m = 2 + 6 i \) , and \( | m - n | - 3 \sqrt { 10 } \) , where \( n \) is a complex number. a. What is the minimum value of the modulus of \( n \) ? b. Provide one example of the complex number, \( n \) . Answer. 

Answer

Step-by-step explanation: Suppose \( m = 2 + 6 i \) , and \( | m + n | = 3 \sqrt { 1 } 0 \) 

The modulus sign means \( m + n \) can either be positive or negative as shown. If it is positive:.2+6i+n \( = 3 \sqrt { 1 } 0 \) 

\( n = 3 \sqrt { 1 } 0 - ( 2 + 6 i ) \) 

\( n = 3 \sqrt { 1 } 0 - 2 - 18 \sqrt { 1 } 0 i \) 

\( n = ( - 2 + 3 \sqrt { 1 } 0 ) + \sqrt { 1 } 0 i \) 

b) Example of the complex number is given as \( ( - 2 + 3 \sqrt { 1 } 0 ) + \sqrt { 1 } 0 i \) . This is a complex number because it contains the real part and the imaginary part. 

Solution
View full explanation on CameraMath App.