Question

What are the modulus and the principal argument of − 5 − 5i?​

Answer 1

We have to find the modulus and the principal argument of -5 - 5i.

solution : modulus of any complex number a + ib is given by, √(a² + b²)

so, modulus of -5 -5i = √{(-5)² + (-5)²} = √50 = 5√2

we see, -5 - 5i is in 3rd quadrant (as real part and imaginary part both are negative )

so, argument can be written as tan¯¹(b/a) - π

here, b = -5 , a = -5

so,. argument = tan¯¹(-5/-5) - π = π/4 - π = -3π/4 or -135°

Therefore modulus is 5√2 and argument is -3π/4 or -135°

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