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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §9.4 Complex Numbers, #31 · Complex Numbers · Polar form

(d) If … approaches zero as …, then (… is negative) (the…

True or false, with an example to show why:

(a) If $c_{1} + c_{2}$ is real, the $c$ 's are complex conjugates.

(b) If $∣ c_{1} ∣ = 2$ and $∣ c_{2} ∣ = 4$ then $c_{1} c_{2}$ has absolute value 8.

(c) If $∣ c_{1} ∣ = 1$ and $∣ c_{2} ∣ = 1$ then $∣ c_{1} + c_{2} ∣$ is (at least 1) (at most 2) (equal to 2).

(d) If $e^{c t}$ approaches zero as $t \to \infty$ , then ( $c$ is negative) (the real part of $c$ is negative) ( $∣ c ∣$ is less than 1).

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §9.4 Complex Numbers, #31

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