.Multiply square root of -8 and square root of -2

Question

1.write the number in simplest form, without a negative radicand. square root of -232

 

2.Multiply square root of -8 and square root of -2

 

3. write the quotient in the form a+bi. 3+5i/1+i

 

4. Determine whether the statement is true or false. There is no real number that is a complex number.  

Answer 1

1.√-232=√(4)(-58)=2√-1√58=2i√58

 

2. √-8*√-2=√-1√8√-1√2=√-1√-1√16=-1*4=-4

 

3. (3+5i)(1-i)/(1+i)(1-i)=3+5i-3i-5i^2/1-i^2=3+2i+5/1+1=8+2i/2=4+i

 

4. generally speaking real numbers are distinct from imaginary numbers

    however, an imaginary number is in the form a+bi where a is the real part and bi is the complex part

    so,.....

    if you had the imaginary number 5+0i, this becomes just 5, which is now real,  so number 4. is false