Since it is to the nearest thousand, it would be 4.999
You need 16 tablespoons for 1 cup and 8 tablespoons for a half cup. Therefore you need to have 24 tablespoons of butter to make cake.
Answer:
Its D :)
Step-by-step explanation:
I just plugged them all in and D was the correct formula
It looks like the given complex number is
<em>z</em> = ((1 + <em>i</em> )¹⁰ - 1) / ((1 + <em>i</em> )¹⁰ + 1)
Let <em>w</em> = 1 + <em>i</em>, so we rewrite
<em>z</em> = (<em>w</em> ¹⁰ - 1) / (<em>w</em> ¹⁰ + 1)
Since <em>w</em> * = 1 - <em>i</em>, we get <em>w</em> <em>w</em> * = (1 + <em>i</em> ) (1 - <em>i</em> ) = 1 - (-1) = 2. Multiply <em>z</em> by ((<em>w</em> *)¹⁰ + 1) / ((<em>w</em> *)¹⁰ + 1). This gives
<em>z</em> = (2¹⁰ - 1 + <em>w</em> ¹⁰ - (<em>w</em> *)¹⁰) / (2¹⁰ + 1 +<em> w</em> ¹⁰ + (<em>w</em> *)¹⁰)
Now, writing <em>w</em> in polar form yields
<em>w</em> = √2 exp(<em>i</em> <em>π</em>/4)
==> <em>w</em> ¹⁰ = (√2)¹⁰ exp(<em>i</em> 10<em>π</em>/4) = 2⁵ exp(<em>i</em> 5<em>π</em>/2) = 2⁵ <em>i</em>
Similarly,
<em>w</em> * = √2 exp(-<em>i</em> <em>π</em>/4)
==> (<em>w</em> *)¹⁰ = -2⁵ <em>i</em>
So we have
<em>w</em> ¹⁰ + (<em>w</em> *)¹⁰ = 0
<em>w</em> ¹⁰ - (<em>w</em> *)¹⁰ = 2 × 2⁵ <em>i</em> = 2⁶ <em>i</em>
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Then we end up with
<em>z</em> = (2¹⁰ - 1 + 2⁶ <em>i </em>) / (2¹⁰ + 1) = (1023 + 64<em>i</em> ) / 1025