Expression ((3+i √5)(3-i √5)/(√3+√2 i)-(√3-i √2)) in a+i b form is

Question

Expression ((3+i √5)(3-i √5)/(√3+√2 i)-(√3-i √2)) in a+i b form is (A) 0+i (B) 0-√2 i (C) 0+√2 i (D) 1+0 i

Tardigrade Admin · Accepted Answer

((3+i √5)(3-i √5)/(√3+√2 i)-(√3-i √2)) =(32-(i √5)2/√3+√2 i-√3+i √2) [∵(z1-z2)(z1+z2)-z12-z22] =(9+5/2 √2 i) =(14 i4/2 √2 i)(∵ i4=1) =(7/√2) i3 =(-7 √2/2) i=0-(7 √2 i/2)

Q. Expression $\frac{( 3 + i 5 ) ( 3 - i 5 )}{( 3 + 2 i ) - ( 3 - i 2 )}$ in $a + ib$ form is

$0 + i$

$0 - 2 i$

$0 + 2 i$

$1 + 0 i$

Q. Expression (3​+2​i)−(3​−i2​)(3+i5​)(3−i5​)​ in a+ib form is

0+i

0−2​i

0+2​i

1+0i

(3​+2i​)−(3​−i2​)(3+i5​)(3−i5​)​ =3​+2​i−3​+i2​32−(i5​)2​[∵(z1​−z2​)(z1​+z2​)−z12​−z22​] =22​i9+5​ =22​i14i4​(∵i4=1) =2​7​i3 =2−72​​i=0−272​i​

Q. Expression $\frac{( 3 + i 5 ) ( 3 - i 5 )}{( 3 + 2 i ) - ( 3 - i 2 )}$ in $a + ib$ form is

$0 + i$

$0 - 2 i$

$0 + 2 i$

$1 + 0 i$