"Ich denke arg an dich" is a German phrase that translates to "I'm thinking a lot about you" in English. It is an expression of affection and care, indicating that the speaker has been thinking about the person they are addressing. This phrase is often used to convey feelings of love, concern, or longing for someone. **

When it says arg(z), you have to draw the angle that the complex number z makes with the positive real axis on the complex plane. This angle is measured in the counterclockwise direction from the positive real axis to the line that connects the origin to the complex number z. The value of arg(z) is usually given in radians and lies in the interval (-π, π]. **

When it says arg(z), you need to draw the angle that the complex number z makes with the positive real axis in the complex plane. This angle is measured in a counterclockwise direction and is usually represented by the Greek letter theta (θ). The value of arg(z) can range from -π to π, or 0 to 2π, depending on the convention being used. **

To find the limit of a specific argument function arg(z), you can use the definition of the argument function, which is the angle that the complex number z makes with the positive real axis. As z approaches a specific value, you can visualize the complex number on the complex plane and observe the angle it makes with the positive real axis. If the angle approaches a specific value as z approaches the given value, then that value is the limit of the argument function arg(z) at that point. You can also use the polar form of the complex number to find the limit of the argument function. **

To determine the argument arg(z) for a complex number z, we use the formula arg(z) = arctan(Im(z)/Re(z)), where Im(z) is the imaginary part of z and Re(z) is the real part of z. For example, if z = 3 + 4i, then Re(z) = 3 and Im(z) = 4, so arg(z) = arctan(4/3). Similarly, if z = -2 - 2i, then Re(z) = -2 and Im(z) = -2, so arg(z) = arctan(-2/-2) = arctan(1) = π/4. **

"Ich mag dich" simply means "I like you," while "Ich mag dich ganz arg" means "I like you very much" or "I like you a lot." The addition of "ganz arg" intensifies the feeling of liking someone, making the second phrase more emphatic and stronger in expressing affection. **

The popularity of cycling or skiing can vary depending on the location and time of year. In general, cycling tends to be more popular in urban areas and during the warmer months, while skiing is more popular in mountainous regions and during the winter. However, it's difficult to determine which activity is followed more overall without specific data on participation rates in different regions and seasons. **

The excitement level of ice hockey versus soccer is subjective and can vary depending on personal preferences. Ice hockey is known for its fast-paced, physical nature with constant action and scoring opportunities. On the other hand, soccer is a more strategic game with longer periods of build-up play and intense moments during goal-scoring opportunities. Both sports have passionate fan bases and offer unique thrills, making it difficult to definitively say which is more exciting. **