Divide 100 by 4:
100 / 4 = 25 with remainder 0
When remainder = 0, i^n = i^4 = 1
Last verified on 25-08-2026
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
Addition of 5y + 4 and 3x + 3y + 1
= 5y + 4 + 3x + 3y + 1
= 3x + 5y + 3y + 4 + 1
= 3x + 8y + 5
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
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
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