Complex Number NAT Level - 1 - IIT JAM MCQ

by squaring both side

2ab = –24 ...(2)
By, (1)² + (2)² are get

a² + b² = 25   ...(3)
by adding (1) and (3)
2a² = 18
⇒ a = ±3
and   b = ±4
from (2) product of ab  is negative so
a = +3  and  b = –4
or  a = –3  and  b = 4
so a³ + b³ = 27 – 64 = –37
or a³ + b³ = –27 + 64 = 37
The correct answer is: 37

put  x = 3
but  

So, 
The correct answer is: 1093

Only ω and ω² satisfy 1st equation
So sum of roots ω + ω² = -1
The correct answer is: -1

From figure


The correct answer is: 2.4

for non-real roots 4 - 8λ<0
λ > 1/2
for equilateral triangle 
|z₁ – z₂ | = |z₂ – z₃ | = |z₃ – z₁ |
⇒ 

or 

The correct answer is: 0.667

= –1
The correct answer is: -1

Compare with 
a = 2 + 3i, b = 4

So, radius 
The correct answer is: 3

The correct answer is: -1

iz³ + z² – z + i = 0

z³ – iz² + iz + 1 = 0
z² (z – i) + i(z – i) = 0
(z – i)(z² + i) = 0
(z – i)(z² + i) = 0
z = i or z² = –i
|z| = |i|   or    |z|² = |–i|
⇒ |z| = 1  or  |z|² = 1
So,  |z| = 1
The correct answer is: 1

–3 – x² yi = x²+ y + 4i
So,  x² + y = –3
⇒ y = –3 – x²
x²y = –4
⇒ x² (3 + x² ) = 4
x⁴ + 3x² – 4 = 0

x² = –4, 1 (x is real)
|x| = 1
y = –4   |y| = 4
|x| + |y| = 5
The correct answer is: 5