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## SAT - Math - Complex Numbers

### For i=square root of -1, what is the sum (7+3i) + (-8+9i)? (more)

For i=-1, what is the sum (7 3i) (-8 9i)?

(7+3i) + (-8+9i)

= (7-8) + i(3+9)

= -1 + 12i

### For i=?(-1), what is the quotient (6-2i)/(2+5i) ? (more)

For i=√(-1), what is the quotient (6-2i)/(2 5i) ?

A) 3 - 2i/5
B) 4 - 3i
C) 1/5 2i/3
D) 2/29 - 34i/29

$Q=\frac { 6-2i }{ 2+5i } x\frac { 2-5i }{ 2-5i } \\ \\ =\quad \frac { 12-34i-10 }{ 4+25 } \\ \\ =\frac { 2-34i }{ 29 }$

Mayank 9 months ago

### can you please say me the reason why 1 is not a prime number as well as composite number? Thank you (more)

we can't say 1 as prime as well as composite.

Historically there was a time when 1 was considered a prime number,

But there is a fundamental theorem in Arithmetic which says that "Every positive whole number can be written as a UNIQUE product of primes"

So for example 6 = 2 x 3 (Both two and 3 are primes) (this is unique)

if we considered 1 as a prime

6 = 1 x 2 x 3 or 1 x 1 x 2 x 3  (Does not remain unique)

hence to keep this fundamental theorem intact, 1 is not considered a prime.

But this a good question.

1 is also not a composite number, because it cannot be split into product of two or more primes.