Question

complex numbers of 7+24i
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Answer 1

Answer:

yes it's a complex number

Step-by-step explanation:

real part is 7

imaginary part is 24i

Answer 2

Answer:√(7 - 24i) = ±(4 - 3i)

Step-by-step explanation:

et √(7 - 24i) = x + iy

Squaring on both side, we get

     7 - 24i = (x + iy)2

=> 7 - 24i = x2 - y2+ 2ixy  ............1

On comparing real and imaginary part, we get

x2 - y2 = 7

and 2xy = -24

=> xy = -24/2

=> xy = -12 ..........2

Now, (x2 + y2 )2= (x2 - y2 )2 + 4x2 * y2

=> (x2 + y2 )2 = (7)2+ 4(-12)2

=> (x2 + y2 )2 = 49 + 4 * 144

=> (x2 + y2 )2 = 49 + 576

=> (x2 + y2 )2 = 625

=> x2 + y2 = ±√625

=> x2 + y2 = ±25

=> x2 + y2 = 25 ..........3             {since x2 + y2 > 0}

On solving equation 1 and 3, we get

     x2 = 16 and y2 = 9

=> x = ±4 and y = ±3

From equation 2,

since xy is negative, So x and y are opposite signs.

So, (x = 4 and y = -3) or (x = -4 and y = 3)

Hence, √(7 - 24i) = ±(4 - 3i)