Explanation

|3| = 3, |−3| = 3, and 2² = 4.

|−3²| = |−9| = 9 → 3 − 3 − 4 − 9 = −13.

Last verified on 02-09-2026

Explanation

32 = 2⁵

So, 2^(x+3) = 2⁵

Therefore, x + 3 = 5

x = 2

Last verified on 11-07-2026

Explanation

Divide 100 by 4: 

100 / 4 = 25 with remainder 0

When remainder = 0, i^n = i^4 = 1

Last verified on 25-08-2026

Explanation

Moduli of (3 + 4i)

Formula for modulus of a + bi = sqrt(a^2 + b^2)

Here a = 3 , b = 4

Modulus = sqrt(3^2 + 4^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

Last verified on 25-08-2026

Explanation

Addition of 5y + 4 and 3x + 3y + 1

= 5y + 4 + 3x + 3y + 1

= 3x + 5y + 3y + 4 + 1

= 3x + 8y + 5

Last verified on 25-08-2026

Explanation

Write 32 as a power of 2  

2 x 2 x 2 x 2 x 2 = 32  

So 32 = 2^5  

Compare with the given equation  

2^x = 32  

2^x = 2^5  

If the bases are the same, the powers must be equal  

x = 5

Last verified on 23-08-2026

Explanation

Rule: If n is odd then a^n + b^n is divisible by a + b

Here n = 43 which is odd  

a = 47 , b = 43  

a + b = 47 + 43 = 90

So 47⁴³ + 43⁴³ is divisible by 90

Last verified on 12-08-2026

Explanation

Given: 

y = 2x 

z = 5y

First find z in terms of x:

z = 5y = 5 _ (2x) = 10x

Now substitute in x + 3y + z:

x + 3y + z = x + 3_(2x) + 10x

= x + 6x + 10x

= 17x

Last verified on 05-08-2026

Explanation

Explanation

 Use the formula: (a + b)(a − b) = a² − b²

Here, a = 3x and b = 2

= (3x)² − (2)²

= 9x² − 4