1 Crore+ students have signed up on EduRev. Have you? 
Find the result in the form a + ib of (2√25) / (1+√16)
(34i) / (23i)*(2+3i) / (2+3i) = (6+9i8i+12) / 13=(18/13)+(i/13)
Find the real numbers x and y such that : (x + iy)(3 + 2i) = 1 + i
(x + iy)(3 + 2i) = (1 + i)
x + iy = (1 + i)/(3 + 2i)
x + iy = [(1 + i) * (3  2i)] / [(3 + 2i)*(3  2i)]
x + iy = (3 + 3i  2i + 2) / [(3)^{2} + (2)^{2}]
x + iy = (5 + i)/[ 9 + 4]
= (5 + i) / 13
=> 13x + 13iy = 5+i
13x = 5 13y = 1
x = 5/13 y = 1/13
Express the following in standard form : (2 – √3i) (2 + √3i) + 2 – 4i
Given: (2−√3i)(2+√3i) + 2 − 4i
(2−√3i)(2+√3i) = 7
⇒ 7 + 2  4i
⇒ 9  4i
Find the reciprocal (or multiplicative inverse) of 2 + 5i
2 + 5i
multiplicative inverse of 2 + 5i is
1/(2+5i)
= 1/(2+5i) * ((25i)/(25i))
= 25i/(2)^2 (5i)^2
= 25i/4(25)
= 25i/4+25
= 25i/29
= 2/29 5i/29
Find the real numbers x and y such that : (x + iy)(3+2i) = 1 + i
(x + iy) (3 + 2i)
= 3x + 2xi + 3iy + 3i*y = 1+i
= 3x2y + i(2x+3y) = 1+i
= 3x2y1 = 0 ; 2x + 3y 1 = 0
on equating real and imaginary parts on both sides
on solving two equations
x= 5/13 ; y = 1/13
(i^{997}) = 1/(i^{997}), 1/((i^{4})^{249}) × i
Since (i^{4}) = 1, (i^{4}) / i = (i^{3})
=  i (Since i^{2} = 1 , therefore, i^{3} =  i)
Express the following in standard form : (8  4i)  (2  3i) + (10 + 3i)
(8  4i)  (2  3i) + (10 + 3i)
=> 8  4i + 2 + 3i10 + 3i
=> 8 + 2  10  4i + 3i + 3i =>0 + 2i
Express the following in standard form : (23i)^{2}
(23i)^{2} = 4 + 9 (i)^{2}  2.2.3i
= 4  9  12i since, i^{2} = 1
=  5  12 i
Express the following in standard form : i^{20} + (1  2i)^{3}
Given, i^{20} + (1  2i)^{3}
We knoe that i = √1
i^{2} = 1
Now put the values in given equation
= i^{20} + (1  2i)^{3}
= ( i^{2})^{10} + { 1  8i^{3}  6i + 12i^{2 }}
= 1 +1  8i^{3}  6i + 12i^{2}
=1 +1  8i^{2}.i^{1}  6i + 12i^{2}
=1 + 1 + 8i  6i 12
= 10 + 2i
(i)(3i) +2(i) =3(i^2)2i =3(1)2i =32i since i=√1 =3+(2)i comparing with a+bi,we get b=(2)
For a complex number a+ib, aib is called its:
This is called conjugate of complex no.
z = a+ib. conjugate of z = aib
 sign is put before i
Complete answers is in 3 steps:
1. Conjugate = 3+4i
2. Modulus = √3^2 + 4^2 =5
3. Multiplicative inverse = conjugate/square of modulus = 3+4i/5^2 = 3+4i/25
156 videos176 docs132 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
156 videos176 docs132 tests









