Question

[2+3i/(7-i)(4+2i)=a+ib , then find a^2+b^2

Answer 1

Answer:

given

2+3i/(7−i)(4+2i)

rationalize denominator

∴ 2+3i/(7−i)(4+2i) × (7+i)(4−2i)/(7+i)(4−2i)

= (2+3i) (7+i) (4−2i)/(7^2+1)(4^2+2^2)

= (14+23i−3)(4−2i)/50×20

= (11+23i)(4−2i)/1000

= 90+70i/1000

= A+iB

∴A = 90/1000 ; B = 70/1000

a^2+b^2 = (90/1000)^2 + (70/1000)^2

= (8100/1000000) + (4900/1000000)

= 0.0081 + 0.0049

= 0.013